Unit 3 Linear Functions and Patterns

2

Big Idea: Linear Functions and Patterns

Objective: The student will learn how to interpret graphs

Common Core Mathematics Standard 2

Interpret graphsRead GET READY for the Lesson, p. 53

What does the point B on the graph represent?

About what percent of normal blood flow occurs two days after the injury?

On what does the percent of blood flow depend?

Vocabulary Interpret graphs

function A relation between input and output.

In a function, the output depends on the input.


Coordinate system Used to graph a function

Formed by the intersection of two number lines, the horizontal axis and vertical axis


Vertical axis : y-axis

Horizontal axis : x-axis

Origin : (0, 0)

Ordered pair(x, y)(3, 2)

I / WE / YOU DO Interpret graphs

I / WE DO- Example 1, p. 53

YOU DO-√ Your Progress, p. 53 #1


In the example the blood flow depends on the number of days since the injury.

Independent variable

Dependent variable

The number of days since the injury

The percent of normal blood flow


I DO- Example 2, p. 54

WE DO- √ Your Progress - p.54 #2A

YOU DO - √ Your Progress - p.54 #2B


I / WE DO-Example 3, p. 54

YOU DO-√ Your Progress - p.54 #3

Practice Interpret graphs

Demonstration of learning – p. 56 # 1 - 7p. 56-58 # 10 - 21

14


Objective: The student will learn how to graph linear equations using x and y intercepts


Graph using interceptsRead GET READY for the Lesson, p. 155

If a person consumes an average of 2000 calories per day, how many grams of fat should the person consume?

How can you use the graph to answer the question?

Vocabulary Graph using intercepts

Linear equation

Standard form of a linear equation

The equation of a straight line

I / WE / YOU DO Graph using intercepts


WE DO-√ Your Progress - p. 156 #1A

YOU DO-√ Your Progress - p. 156 #1B


X-intercept

y-intercept

The x-coordinate of the point where the graph of an equation crosses the x-axis

The y-coordinate of the point where the graph of an equation crosses the y-axis.


y-intercept : (0, y)

x-intercept : (x, 0)

(0, 4)

(3, 0)


I DO-Example 2, p. 156





YOU DO-√ Your Progress - p. 157 #3

Practice Graph using interceptsDemonstration of Learning – p. 158 # 1 - 11p. 159-160- Identify linear equations and write in

standard form#12 -17

- Determine intercepts of each function#18 - 23

- Graph a linear equation using a table or intercepts

#24 – 32- Applications

#33 – 38; 53 - 55

25


Objective: The student will learn how to solve problems using slope of a line.


Slope of a lineRead GET READY for the Lesson, p. 187

What is the slope of the roof if the rise is 10 and the run is 6?

What might the rise and run be for a roof with a slope of 2?

Vocabulary Slope of a line

Rate of change

rate of change =

A ratio that describes, on average, how much one quantity changes with respect to another quantity

Slope of a lineThe table on p.187 shows the distance a person has walked for various amounts of time

rate of change =

rate of change =

rate of change =

This means that the person walked 4 feet per second

I / WE / YOU DO Slope of a line




Slope of a line

slope =

(4, 5)

(1, 3)

I / WE / YOU DO Positive slope of a line




I / WE / YOU DO Negative slope of a line




I / WE / YOU DO Zero slope of a line




I / WE / YOU DO Undefined slope of a line




I / WE / YOU DO Find coordinates given slope




Practice slope of a lineDemonstration of Learning p.192 #1-13p. 192-195 - Rate of change from a table or graph

#14-19- Slope of a line passing through 2

points #20 – 31; 36 - 39, 62

- Find coordinates given slope #32-35; 44-47

- Applications #48-57

38


Objective: The student will learn how to write and graph a linear function in slope-intercept form.


Write & graph linear functionsRead GET READY for the Lesson, p. 204

Does the line have a positive slope or negative slope?

What do x and y represent in the equation?

A checking plan offered by a bank includes a $10 monthly service fee and a $0.20 per check fee for accounts with an average daily balance of less than $2000. What equation describes this plan?

Vocabulary Write & graph linear functions

Slope intercept form of a linear equation

where m is the slope and b is the

y-intercept

(0, b)

O

y = mx + b

I / WE / YOU Write & graph linear functions

I / WE DOExample 1, p. 204





WE DO-√ Your Progress - p. 205 #3C


YOU DO-√ Your Progress - p. 205 #3D

Vocabulary Write & graph linear functions

Starting point

Rate of change

The y- intercept of a linear equation that models real-world data.

The slope of a linear equation that models real world data.

Practice Write & graph linear functions

p. 207 - 208- Write a linear function given slope and y-

intercept#11 – 17, 39 - 44

- Write a linear function given a graph#18 – 23

- Graph a linear function given an equation.#24 – 32

- Applications#33 -38

47


Objective: The student will learn how to write a linear function and use it to solve problems.


Linear functionsRead GET READY for the Lesson, p. 213

How do you know that the slope is 7000?

A biologist is studying how fast a bacteria grows. The population of bacteria has an average growth of 200 bacteria per hour. Describe the graph that demonstrates the growth.

I / WE / YOU Linear functions



RECALL - Vocabulary Linear functions

Standard form of a linear equation

RECALL Vocabulary Write & graph linear functions

Slope intercept form of a linear equation

where m is the slope and b is the

y-intercept

(0, b)

O

y = mx + b

Practice Linear functionsDemonstration of Learning – p. 216 #1-9

- Write a linear function given a point and the slopep. 217 #10 – 17; p. 223 # 12 – 17

- Write a linear function given 2 pointsp. 217 #18 – 25; 30 – 35

- Write a linear function in standard formp. 223 #20 – 27

- Write a linear function in slope-intercept formp. 223 #28 – 35

- Applicationp. 217 #8, 9, 26 – 29; p. 224 #37, 38, 40, 41

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Objective: The student will learn how use lines of best fit to make and evaluate predictions.


Lines of best fitRead GET READY for the Lesson, p. 227

Does the line have positive or negative slope? How do you know?

What would you do to find the equation of that line?

Vocabulary Lines of best fit

Scatter plot A graph in which two sets of data are plotted as ordered pairs .

Used to investigate a relationship between two quantities.


Scatter plot with a positive correlation

O

positive slope


Scatter plot with a negative correlation

O

negative slope


Scatter plot with no correlation

O

I / WE / YOU Lines of best fit



Algebra LAB p. 228 Lines of best fit

Is there a relationship between the length of a person’s foot and their height?

Make a prediction. What do you think the relationship between the length of person’s foot and their height is?

Describe the relationship between the length of a person’s foot and their height in terms of independent and dependent variables.

Algebra LAB p. 228 Lines of best fitFoot length (cm) Height (cm) Foot length (cm) Height (cm)

I / WE / YOU Lines of best fit

I / WE DO- Example 2, p. 229- Example 3, p. 230

YOU DO-√ Your Progress - p. 229 #2- √ Your Progress - p. 230 #3

Practice Lines of best fit

- Demonstration of Learning p. 230 #1 -7

- Applicationp. 231 – 232 #8 - 27

Unit 3 Linear Functions and Patterns

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Transcript of Unit 3 Linear Functions and Patterns