Download - · Web viewChapter 6 – Linear Functions. Part A: Graphing and Modeling. Unit 6 - Vocabulary. rate. average rate of change. interval. linear function. slope of a line. graph.

Chapter 6 – Linear

Functions

Part A: Graphing and Modeling

1

Unit 6 - Vocabulary

1) rate

2) average rate of change

3) interval

4) linear function

5) slope of a line

6) graph

7) slope-intercept form of the equation

8) intercepts (x and y)

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Day 1: Average Rate of Change F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Warm-Up

Give an example of a rate in everyday life.

What is the rate of change?

A rate of change is a ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.

Rate of Change= change∈dependent variablechange∈independent variable

=¿−¿¿−¿

Model Problem

The table shows the average temperature (°F) for five months in a certain city. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate?

Independent Variable (x) ______________________ Dependent Variable (y)_________________

From month 2 to month 3




Notes

Because this is a rate of change, we express the final answer as a fraction or as a statement using the word “per.” Always reduce the fractions.

When subtracting, make sure you write the “to” number first before the “from” number.

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Exercise A

The table shows the balance of a bank account on different days of the month. Find the rate of change during each time interval. During which time interval did the balance decrease at the greatest rate?

Independent Variable ___________________ Dependent Variable __________________

From day 1 to day 6 _________________________________ = ________________

From day 6 to day 16 ________________________________ = ________________

From day ____ to day ____ ______________________________ = ________________

From day ____ to day ____ ______________________________ = ________________

Determining Rate of Change from a Graph

When looking at a graph, we can use the following formula for the average rate of change:

f ( x2 )− f ( x1)x2−x1

=y2− y1

x2−x1

Model Problem B

The graph at right shows the distance that a vehicle travels over time. Find the average rate of change for each interval.

Hour 0 to Hour 1: Hour 1 to Hour 2:

Hour 2 to Hour 3: Hour 3 to Hour 4:

The average rate of change in this example is measuring the ________ of the vehicle.

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Model Problem B continued

1) During which interval of time was the average rate of change the greatest? The least?

2) How do you know this by looking at the graph?

3) Calculate the average speed of the vehicle from hour 1 to hour 4. Was the vehicle traveling at this speed the whole time? Explain.

Exercise B

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Exercise B (continued)

The table shows the number of bikes made by a company for certain years.

a) Plot the points on the graph provided and connect them. Think about: Which variable is the independent variable? Which is dependent? By what units (1’s, 5’s, 10’s, etc) should you count to fit in all the ordered pairs?

b) Using this graph, find the average rate of change for each time period. c) During which time period did the number of bikes increase at the fastest rate?

The interval that had the highest average rate of change is between year _________ and year ___________ .

Homework – Day 1

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From year 1 to year 2




2)

a) Graph the data on the axes below.

b) Calculate the rates of change during each 1-hour interval.

From 0 to 1 hour From 3 to 4 hours

From 1 to 2 hours From 4 to 5 hours

From 2 to 3 hours From 5 to 6 hours

c)

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Day 2: Identifying Linear Functions F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

Warm-Up

Use the vertical line test to tell whether the graph of each relation is a function.

1) 2)

3) 4)

What is a Linear Function? How do We Know a Function is Linear?

We already learned that a function is a relation in which each value in the domain (x) is paired with exactly one value in the range (y). The vertical line test works because if a vertical line hits a graph twice, it means that a given value for x is paired with more than one y.

A linear function is a function whose graph forms a straight line. Of the functions that we identified above, we can see that only a few form straight lines. In this lesson, we will learn what makes a given function linear.

Method 1: Use the graph. Perhaps the most obvious way to tell if a function is linear is to use the graph. Remember, first you must decide if it is a function, then if it is, tell whether or not it is linear.

Exercise #1 Which of the graphs in the Warm-Up depicts a linear function?

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Method 2: Use the table of values.

Let’s look at some of the graphs you did in the Calculator Exercise and see what makes some linear and others not.

Examples of Linear Functions

The following functions are linear functions. Their tables are listed below. Notice that a constant change in x corresponds to a constant change in y. This is the way you tell that a function is linear from its table of values.

These functions are linear functions because _______________________________________________

___________________________________________________________________________________

Examples of Functions that are Not Linear

y=|x−3| y = x2 + 2x – 3 y = x3

x y

0 3

1 2

2 1

3 0

4 1

5 2

6 3

9

Explain why these functions are NOT linear:

y = 3x + 4

x y

-3 -5

-2 -2

-1 1

0 4

1 7

2 10

3 13

y =−12 x + 3

x y

-3 4.5

-2 4

-1 3.5

0 3

1 2.5

2 2

3 1.5

y = 2x

x y

-3 -6

-2 -4

-1 -2

0 0

1 2

2 4

3 6

x y

-4 5

-3 0

-2 -3

-1 -4

0 -3

1 0

2 5

x y

-2 -8

-1 -1

0 0

1 1

2 8

Exercise Tell whether each set of ordered pairs depicts a linear function. If it does, state the rate of change.

1) 2)

4) Complete the table below so that the ordered pairs depict a linear function with a constant rate of change equal to 3.

Slope: A Property of a Linear Function

10

x y

0 -3

4 0

8 3

12 6

16 9

x y

3 5

5 4

7 3

9 2

11 1

x y

-4 13

-2 1

0 -3

2 1

4 13

x y

0 3

2 7

4 11

8 19

14 31

x 0 2 3

y 4 10

Recall that the linear function’s rate of change is always the same, or constant. This constant rate of change gives the linear function its shape and is called the slope of the line.

Finding the Slope of a LineBy counting boxes on a graph: By using two points on a line (x1, y1) and (x2, y2)

slope= riserun slope= change∈ y−values

change∈x−values=

y2− y1

x2−x1

Method 1: Counting Boxes

Model Problems

1) Find the slope of the line shown. 2) Find the slope of the line below.

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3)

Practice Find the slope of each line.

5) Find the slope of the line that contains (2, 5) and (8, 1).

6) Find the slope of the line that contains (5, –7) and (6, –4).

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7) Look back at Questions #1-4. Which lines had a slope that was a positive number? A negative number? Zero?

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Positive, Negative, Zero, or No Slope

Positive Slope Negative Slope

As x increases, y increases. As x increases, y decreases.The line rises from left to right. The line falls from left to right.

Zero Slope No SlopeAs x increases, y doesn’t change. If the slope is found, a zero is in The line is horizontal. the denominator, which is makes the slope undefined.

Summary

Exercise

Tell whether each line has positive, negative, zero, or no slope (undefined).

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Summary

The rate of change is the change in the y-values divided by the change in x-values.When the rate of change of y to x is constant, it defines a linear function and is called the slope of a line. It is given by:

slope= riserun

=y2− y1

x2−x1

A line has positive slope if it rises from left to right.A line has negative slope if it falls from left to right.A line has zero slope if it is horizontal.A line has no slope (undefined slope) if it is vertical.

Exit Ticket

Find the slope of the line that contains (5, 8) and (4, –4).

Homework in textbook

p. 301 #26-29

p. 314 #9-12

p. 324 #11-15, 21-23

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Day 3: The Slope-Intercept Form of the Equation A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

F-LE.1 a. Prove that linear functions grow by equal differences over equal intervals.

F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Warm-Up

Sketch the graph of the function y = 2x + 3 using the partial domain given in the table of values.

x y = 2x + 3 y (x, y)-1

0

1

2

Exploration

1) What type of function is this? _______________________________

What characteristics of the points make the graph have this shape?

2) What is the slope of this line? _______________________

Show where is this reflected in the equation y=2x+3.

3) Where does the line hit the y-axis? ______________________________________

Show where is this reflected in the equation y=2x+3.

4) Plot the point (3, 7) on the same set of axes. (Do not connect it with your graph.)Is the point (3, 7) on the line? Why or why not? ____________________________

5) If the chart was continued to include x = 3, what would the value of y be? How do you know?

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Exercise

Sketch the graph of each function using the partial domain provided and answer the questions that follow.

1)

x y = 3x + 1 y (x, y)-1

0

1

2

2)

x y = 4x y (x, y)-1

0

1

2

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What is the slope of this line? ___________________

Where is this reflected in the equation y=3 x+1?

Where does the graph hit the y-axis? _______________

Where is this reflected in the equation y=3 x+1?

What is the slope of this line? ___________________

Where is this reflected in the equation y=4 x?

Where does the graph hit the y-axis? _____________

Where is this reflected in the equation y=4 x?

3)

x y = - 2x - 2 y (x, y)-1

0

1

2

What exactly is an equation? What does it do?

An equation is a rule that states the relationship between two variables, x and y. We already know that x is the input and y is the output. The equation is the function rule that shows how x gets mapped to y.

For example, in the equation y = 2x + 3, each y-value is 3 more than 2 times each x-value.

x -1 0 1 2y 1 3 5 7

A graph is a picture of a function. Each x is paired with the y that is obtained by using the function rule. But besides telling us a relationship between x and y, a linear equation can also tell us valuable information about the graph when it is written a certain way.

Let’s look at this equation more closely.

What can a linear equation tell us about its graph?y=2 x+3

These two pieces of information taken together:

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This number can tell us the SLOPE of the line.

This number can tell us where the graph hits the y-axis. This point is called the Y-INTERCEPT.

What is the slope of this line? ______________________

Where is this reflected in the equation y=−2x−2?

Where does the graph hit the y-axis? ________________

Where is this reflected in the equation y=−2x−2?

Define a unique line in the coordinate plane. This means that no other line will have the same slope and y-intercept.

Is enough to graph that line (without using a table of values)!

This form of the equation is called the slope-intercept form of the equation.

The Slope-Intercept Form of the Equation of a Line

Model Problems

Find the slope and the y-intercept of each line.Then use the slope and y-intercept to sketch the graph of the line.

1) y=3 x−5 2) y=−2x+ 3

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3) 3 x−2 y=6 4) x+6 y=18

Practice

Find the slope and the y-intercept of each line.Then use the slope and y-intercept to sketch the graph of the line.

1) y=2 x−5 2) y=−x+ 3

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Remember! The slope-intercept form of the equation is y=m x+b

3) 3 y+2 x=15 4) x− y=7

Determining if a point is on the graph

Model Problems

A) Is the point (4,10) on the graph of the line given by y=3 x−2 ?

B) Is the point (-3, 4) on the graph of the line given by y=−2 x+4 ?

C) Find the value of x if the point (x, 7) is on the graph of 3 x+ y=10.

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Exercises

A) Is the point (6,3) on the graph of the line given by y=x+4 ?

B) Is the point (-2, 4) on the graph of the line given by y=−12

x+3 ?

C) Find the value of x if the point (x, 5) is on the graph of 2 x+4 y=8.

Essential Questions

Today we learned that the slope-intercept form of the equation tells us important information about the graph of a function.

y=mx+b

1) Which parameter gives the slope of the line?

2) Which parameter gives the y-intercept of the line?

3) How can we show algebraically that a point is on the graph of a function?

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Homework

Tell if each point is on the graph of the equation given.

1) Is the point (-5, 4) on the graph of the line given by y=3 x+2 ?

2) Is the point (3, -1) on the graph of the line given by 2 x−7= y?

3) Find the value of k if the point (k, -10) is on the graph of y=34

x+14.

4)

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Day 4: Real-World Applications of the Slope-Intercept FormA-CED.16 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

F-LE.1 b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

Warm-Up

Consider the equation y=−2 x+8. Where does this graph hit the y-axis? What is the slope of this line? Is the point (4,0) on this line?

Model Problem

1) Write a function rule that represents the cost of the dinner as a function of the number of students.

___________________________________

2) What is the slope of this line? ________________ Show how to arrive at this slope using the graph above. What does the slope represent in the context above?

3) What is the y-intercept of this line? Where is this on the graph? What does the y-intercept represent in the context of the problem?

4) Find the cost for 50 students to attend this dinner.

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Exercise

1) Write a function rule that represents the distance that Laura traveled as a function of the number of hours she hiked on the second day. ________________________________

2) What is the slope of this line? ________________ Show how to arrive at this slope using the graph above. What does the slope represent in the context above?

3) What is the y-intercept of this line? Where is this on the graph? What does the y-intercept represent in the context of the problem?

4) What will be Laura’s total distance if she hiked for 6 hours on the second day?

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A caterer charges a $200 fee plus $18 per person served. The total cost of the catering fees as a function of the number of guests is shown in the graph at right.

1) Write a function rule for the total cost of the catering.

2) Identify the slope and the y-intercept in this equation and describe their meanings.

3) If you have $4,000, can you have an event for 200 guests? Explain.

1) Write a function rule for the total cost of the organizers fee as a function of the number of hours worked.

2) Identify the slope and the y-intercept and describe their meanings.

3) Find the cost if the organizer works 12 hours.

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SummarySlope-Intercept Form of the Equation of a Line

y=mx+bSlope = m Y-intercept = b Tells theconstant rate of change∈ y vs . x Tells how much is added/subtracted Look for “per,” “for each,” or “for every”

Tells the starting/initial value. Does not change (fixed) Look for “starting fee,” “initial amount,” etc.

The equation of a line tells the relationship between the x-values and the y-values in a linear function.

A point is on the graph of a line if it makes the equation of the line true.

Homework

1) A school orders 25 desks for each classroom, plus 30 spare desks. The total number of desks ordered as a function of the number of classrooms is shown below.

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2) A company that manufactures radios first pays a start-up cost, then spends a certain amount of money to manufacture each radio. The cost of manufacturing r radios is given by the function c (r )=5.25 r+125. State the meaning of each variable or constant in the context of the problem.

c (r ) _______________________________________________________________________

r _______________________________________________________________________

5.25_______________________________________________________________________

125 ______________________________________________________________________

3) You are a comic-book collector and have a subscription to a weekly comic book delivery service. Each month, you have to pay a certain amount to have the new issue delivered. You have saved $300 to pay for these comic books. The function c (b )=300−2.50 b models the amount of money you have remaining in your comic book account. State the meaning of each variable or constant in the context of the problem.

c (b) _______________________________________________________________________

b _______________________________________________________________________

300 _______________________________________________________________________

2.50 _______________________________________________________________________

Why is the 2.50 negative? ______________________________________________________

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Day 5: Writing the Equation of a Line F-BF.1 Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

Warm-Up

1) Find the slope and the y-intercept of the line given by the equation 4 x+3 y=12. 2) Sketch the graph of the line with a slope of

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and that passes through the point (0, -4).

What is special about this point?

Model Problem A Writing an equation in slope-intercept form

Write the equation of the line that has a slope of 43 and passes

through the point (3, 2). Graph the line.

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Exercise A

Write an equation of a line that has a slope of -2 passing through the point (3, -1). Graph the line.

Model Problem B

Write the equation of the line that passes through (-1, 3) and (1, -1).

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Reminder: If the slope is not given to you, there will always be a clue!

Exercise B

Write the equation of the line containing the points (3, 5) and (4, 7).

Model Problem C

The chart below depicts a linear function. Write an equation of this line.

Exercise C

Write an equation of the line represented below.

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x 1 2 3 4 5

y -5 -3 -1 1 3

x -1 1 3 5

y 4 8 12 16

Model Problem D Exercise D

Write an equation of the line shown below. Write an equation of the line shown

below.

ise

Summary

To write an equation in slope-intercept form, follow these steps:

Step 1 Find the slope using the formula, Step 3 Plug in the point in for xthe graph, or a table. and y. Solve for b.

Step 2 Write y = mx + b Step 4 Rewrite y = mx + b with the and plug in the slope. slope and y-intercept.

Challenge! Line l contains the points (2, 3) and (6, 5). Determine if the point (-8, -2) lies on line l.

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Homework

1. Write the equation of the line that has the given slope and that passes through the given point.

a. m = 3, (1,5) b. m = 32 , (-2, 8)

2. Write the equation of the line that passes through the given points.

a. (12, -5) and (-4, -1) b. (0, 3) and (2, 9)

3. Write the equation of the line shown in each table.

Equation: _______________________ Equation: _______________________

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4) Write an equation of each line shown below.

_________________________________ ___________________________________

5) Review: Graph each line.

x=−2 y=0 x=1

6) Write the equation of the vertical line that passes through the point (9, 4). Does this line have a y-intercept? Explain.

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7) The graph below shows the yearly total cost for joining the club and playing a certain number of games throughout the year.

a) Write a function rule that illustrates the total cost of joining the club.

b) What is the total cost of joining the club and playing 10 games throughout the year?

8) Does the following table below depict a linear function? If so, write a rule in function notation describing the relationship between x and y.If not, explain why it is not a linear function.

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Day 6: More Practice with Real-World ApplicationsA-CED.16 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

F-LE.1 b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

Warm-Up

The owner of a small computer repair business has one employee, who is paid an hourly rate of $22. The owner estimates his weekly profit using the function P(x )=8600−22 x . Tell what each variable or constant represents.

P ( x ):______________________________________________________________________

x : _________________________________________________________________________

22: ________________________________________________________________________

8600: ______________________________________________________________________

Remember

Slope-Intercept Form of a Linear Equation f ( x )=mx+b

f ( x )∨ y - what the problem is about

x−¿what f depends on

m – the constant rate of change (look for per, each, every)

b−¿the starting point or fixed amount

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Concept: Linear FunctionsBy the end of this lesson, you should be able to express a linear function that is presented

in any one of these four ways:

Equation Table

Graph Situation

Problem Solving

1) Using a graph. The Martins are getting new carpet for their living room. The total cost for carpeting is graphed below as a function of the area covered.

a) Find the slope of this line. (Watch the units!!) What does the slope represent?

b) Find the y-intercept of this line. What does it represent?

c) Write a function rule for the total cost of carpeting the Martins’ living room.

d) Can the Martins afford to carpet their entire 1,000 sq. ft. house if they have only $4,000 to spend? Explain your reasoning.

e) The carpet company decides to waive the administrative fee but keep the cost per square foot the same. Sketch the graph that represents this new cost function. Can the Martins afford to carpet their home now?

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2) Using a table. Each day, Toni records the height of a plant for her science lab. Her data are shown in the table below.

The plant continues to grow at a constant daily rate. Write an equation to represent h(n), the height of the plant on the nth day.

3) Interpreting a situation. Caitlin has a movie rental card worth $175. After she rents the first movie, the card’s value is $ 172.25 . After she rents the second movie, the card is worth $169.50. After she rents the third movie, the card is worth $166.75. Assuming the pattern continues, write an equation to define A(n), the amount of money on the rental card after n rentals. (Hint: Make a table and determine the equation the same way you did in #2.)

Caitlin rents a move every Friday night. How many weeks in a row can she afford to rent a movie, using her rental card only? Explain how you arrived at your answer.

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4) The graph shows the cost of a smartphone plan.

a) Find the slope of this line. What does the slope represent?

b) Find the y-intercept of this line. What does it represent?

c) Write a function rule for the total cost of using the smartphone under this plan.

5) In 1960, the world record for the men’s mile was 3.91 minutes. In 1980, the record time was 3.81 minutes.

a) Write a linear model that represents the world record (in minutes) for the men’s mile as a function of the number of years since 1960.

b) Use the model to estimate the record time in 2000 and predict the record time in 2020.

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6) A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $75 per hour.

a) Write a linear model that represents the total cost of recording an album as a function of studio time (in hours).

b) Is it less expensive to purchase 12 hours of recording time at the studio or a $750 music software program that you can use to record music on your own computer? Explain.

7)

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8) Describe a real-life situation that can be modeled by a linear function whose graph passes through these points.

9) Andie, Bryan, and Caitlyn are siblings that each receive money for a holiday and then spend it at a constant weekly rate. The graph describes Andie’s spending, the table describes Bryan’s spending, and the equation y=−22.5 x+90 describes Caitlyn’s spending. The variable y represents the amount of money left after xweeks.

Andie’s Spending Bryan’s Spending

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Day 7: Horizontal and Vertical LinesA-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Warm-Up

Sketch the graph of the line containing the points (-2, 4) and (5, 4).

a. What do you notice about the coordinates of these points?

b. What is the equation of this line?

c. What is the slope of this line?

Sketch the graph of the line containing the points (-2, 4) and (-2, 0).

a. What do you notice about the coordinates of these points?

b. What is the equation of this line?

c. What is the slope of this line?

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Equations of Horizontal and Vertical Lines

Horizontal Lines Vertical Lines

Horizontal lines are parallel to the x-axis.

They have a slope of zero.

Vertical lines are parallel to the y-axis.

We say their slope is undefined, or that they have no slope.

Exercise

1) For each equation given, answer the following questions:

a) Is it horizontal, vertical, or neither?b) What is the slope of this line?c) Sketch the graph of this line.

x=2 y=−5 y=x

a. _______________

b. _______________

c.

d. _______________

e. _______________

f.

g. _______________

h. _______________

i.

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2) Sketch the graphs of:

x=4 y=3 x=0

𝑦 = −3 x=4 y=0

Model Problem B

Write the equation of a line that is:

a) Parallel to the x-axis and passes through (5, 6).

b) Parallel to the y-axis and passes through (5, 6).

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Exercise B

Write an equation of the line that is:

1) Parallel to the x-axis and passes through the point (-3, -2). _________________________

2) Parallel to the y-axis and passes through the point (7, -1). _________________________

Challenge

Write the equation of a line that is parallel to the line given by 5 x+ y=3 and whose y-intercept is the same as the line given by 4 x+3 y=9.

Homework Cumulative Review

1) For each equation given, answer the following questions:a) Is it horizontal, vertical, or neither?b) What is the slope of this line?c) Sketch the graph of this line.

x=4 y=−3 y=2x

a) _______________

b) _______________

c)

a) _______________

b) _______________

c)

a) _______________

b) _______________

c)

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2)

3)

4)

5)

46

Day 8: Graphing by Intercept Method

F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

Warm-Up Match each equation with its graph. Explain your reasoning.

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Identifying Intercepts Identify the x and y-intercepts. Label their coordinates on the graph.

1)

x-intercept ____ y-intercept _____

2)

x-intercept _______ y-intercept ________

Using X- and Y-Intercepts to Graph Lines

Use the intercept method to graph when using the slope-intercept method is not practical.

Model Problem A

Graph the equation 10 x+6 y=100 on the axes provided. Label at least two ordered pairs that are solutions on your graph.

Step 1: Find the x-intercept.

Substitute y=0 into the equation. Solve for x.

x-intercept___________________

Step 2: Find the y-intercept.

Substitute x=0 into the equation. Solve for y.

y-intercept___________________

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Exercise A

Graph the solution set of y=9.5 x+20in the coordinate plane. Label at least two ordered pairs that are solutions on your graph.

Step 1: Find the x-intercept.

Substitute y=0 into the equation. Solve for x.

x-intercept___________________

Step 2: Find the y-intercept.

Substitute x=0 into the equation. Solve for y.

y-intercept___________________

Model Problem B First-Quadrant Graphs

Jennifer started with $50 in her savings account. Each week

she withdrew $10. The amount of money in her savings account

after x weeks is represented by the function f ( x )=50−10 x

a) Find the intercepts and graph the function.

b) What does each intercept represent?

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Exercise Ba)

a) Write an equation to represent this situation.

b) Graph this equation on the set of axes below. (Hint: Pay attention to your domain and range!!)

c) Determine and state one combination of hours that will allow Edith to earn the $80.

_____________ hours at after-school job _____________ hours as library assistant

2) A small town is trying to establish a transportation system of small and large vans. They have $100,000 to spend to purchase these vans. Small vans cost $10,000 and large vans cost $25,000.

a) Write an equation to represent this situation.

b) Sketch the graph of this equation on the axes at right.50

1) Edith babysits for x hours per week after school at a job that pays $4 per hour. She has accepted a job as a library assistant that pays $8 per hour working y hours per week. She will work both jobs, and she needs to earn $80 to buy a new jacket that she saw in her favorite store.

c) What does the x-intercept represent?

d) Determine and state one combination of vans that the town can buy.3) Kristen was on the stationary bike at the gym. The chart represents how much distance she covered during

the time she was working out.

a) What are the x- and y-intercepts of this function?

b) What do they represent?

4)

5)

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(1) (2) (3) (4)

Day 9 - Review of Chapter 6Slope/Rate of Change

2)

From Hour 1 to Hour 8: _________________________________________

3) Albert (A) went for a run and Bill (B) went for a walk at lunchtime. Their distances (in miles) and times (in minutes) are recorded in the graph at right. How much faster was Albert’s speed than Bill’s, in miles per minute?

4)

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5) On each pair of axes, sketch a line that has the type of slope described.

positive negative zero undefined

6) Determine whether the function described below is linear. Using the words rate of change and slope, explain your choice.

Is a Point on the Line?

7)

The Equation of a Line

8)

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Writing the Equation of a Line

9)

10) Write the equation of a line passing through (3, 1) and (4, 3).

11) Write the equation of the line that contains the points below.

d=¿¿

12) The line at right describes the total yearly cost of playing golf games at the Shadybrook Golf Course. The cost includes a membership fee and the price of playing golf games.

a) Write a function rule to express the total cost of belonging to and playing at Shadybrook as a function of games played.

b) Explain the meaning of the slope and y-intercept.

Horizontal and Vertical Lines55

13) Given: y=5

a. Sketch the graph.

b. What is the slope of this line?

c. Is it parallel to the x-axis or the y-axis?

14) Given: x=2

a. Sketch the graph.

b. What is the slope of this line?

c. Is it parallel to the x-axis or the y-axis?

15)

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