Graphing Linear Equations

Vocabulary

1. Slope 2. Graph3. Coordinate Plane4. Y- Intercept5. X-Intercept6. Y-Axis7. X-Axis8. Linear Relationship9. Quadrant10. Origin

Slope

• Positive or Negative• Ascending/Increasing +• Descending/Decreasing –• Bridge Thickness -------slope is positive• Bridge Length---------slope negative• Slope is always m

Problem 1.4 Ms. Chang’s Class decides to use

their walkathon money to provide books for the children’s ward at the hospital. They put the money in the school safe and withdrawl a fixed amount each week to buy new books. To keep track of the money, Isabella makes a table of the amount of money in the account at the end of each week.

Week Amount of Money at the End

of Each Week0 $144

1 $132

2 $120

3 $108

4 $96

5 $84

1.4 Recognizing Linear Equations

A. 1. How much money is in the account at the start of the project?2. How much money is withdrawn from the account each week?3. Is the relationship between the number of weeks and the amount of money left in the account a linear relationship? Explain.

Relationships

• X – line \ /• X squared – U • Absolute Value - V• X cubed - S

1.4 Recognizing Linear Equations

4. Suppose the students continue withdrawling the same amount of money each week. Sketch a graph of this relationship. When will the students run out of money?

5. Write an equation that represents the relationship. Explain what information each number and variable represents.

1.4 cont.

Y = -12X + 144 Y = the amount of money

0 = -12X +144 X= The amount of weeks

-144 = -12X

12 weeks = XThe class will run out of money in 12 weeks.

1.4 Recognizing Linear Equations

B. Mr. Mamer’s class also raised money from the walkathon. They use their money to buy games and puzzle’s for the children’s ward. Sade uses a graph to keep track of the amount of money in their account at the end of each week.

1.4 Cont.X Y

0 200

1 175

2 150

3 125

4 100

5 75

6 50

7 25

8 0

9 -25

10 -50

1.4 Recognizing Linear Equations

1. What information does the graph represent about the money in Mr. Mamer’s class account?2. Make a table of the data for the first 10 weeks. Explain why the table represents a linear relationship.3. Write an equation that represents the linear relationship. Explain what information each number and variable represents.

1.1 Through 1.4 Application Problems

1. Hoshi walks 10 meters in 3 seconds.

a. What is her walking rate?b. At this rate, how long does it take her to walk 100

meters?c. Suppose she walks this same rate for 50 seconds.

How far does she walk?d. Write an equation that represents the distance d

that Hoshi walks in t seconds.

X Y

1 3 1/3

2 6 2/3

3 10

4 13 1/3

5 16 2/3

6 20

7 23 1/3

8 26 2/3

9 30

10 33 1/3

M = 3 1/3 b= 0 y= 3 1/3X + -0.0027

2.1 Point of Intersection

POINT OF INTERSECTION:

Where two or more graphs meet or cross

2.1 Point of Intersection

In Ms. Chang’s class, Emilie found out that her walking rate is 2.5 meters per second. When she gets home from school, she finds out her little brother, Henri, walks 100 meters. She figures out that Henry’s walking rate is 1 meter per second.

2.1 Point of Intersection

Henri challenges Emilie to a walking race. Because Emilie’s walking rate is faster, Emilie gives Henry a 45-meter head start. Emilie knows her brother would enjoy winning the race, but he does not want to make it obvious that she is letting him win.

2.1 Point of Intersection

a. How long should the race be so that Henri will win at a close race?

b. Describe your strategy for finding your answer to question a and provide evidence.

2.1 Applications

1. Grace and Allie are going to meet at the fountain near their houses. They both leave their houses at the same time. Allie passes Grace’s house on her way to the fountain.

a. Allie’s walking rate is 2 meters per secondb. Grace’s walking rate is 1.5 meters per second.

2.1 Applications

a. How many seconds will it take Allie to reach the fountain?

b. Suppose Grace’s house is 90 meters from the fountain. Who will reach the fountain first. Allie or Grace? Explain.

2.3 Comparing Costs

Coefficient: the number that multiplies by a variable.

2X The coefficient is 2(1/2)X The coefficient is (1/2)0.75X The coefficient is 0.75-4X The coefficient is -4(-1/3)X The coefficient is (-1/3)-0.333X The coefficient is -0.333

2.3 Comparing Costs

Ms. Chang’s class decides to give T-shirts to each person who participates in the Walkathon. They receive bids for the cost of the T-shirts from two different companies. Mighty Tee charges $49 plus $1 per T-shirt. No Shrink Tee charges $4.50 per T-shirt.

2.3 Comparing Costs

Ms. Chang’s class decides to give T-shirts to each person who participates in the Walkathon. They receive bids for the cost of the T-shirts from two different companies.

-Mighty Tee charges $49 plus $1 per T-shirt. -No Shrink Tee charges $4.50 per T-shirt.

2.3 Comparing Costs

Step 1: Make an X and Y equation for each company.

Step 2: Change X to n (Number of Shirts) and Y to C (Cost)

2.3 Comparing Costs

Step 3: Analyze the Equations

What does the coefficient of n mean?

What does the y-intercept mean?

2.3 Comparing Costs

Step 4: Look at the Basic Questions

If each company sells 20 T-shirts, what is the cost? (if x=20, what is y?)

If the school has $120 to spend on T-shirts, which company can the school buy the most T-shirts at? (if y=120, what is x?)

2.3 Comparing Costs

Step 5: Find the Point of Intersection

For what number of T-shirts is the cost of the two companies equal?

Strategies to Use:1. Graph and Trace2. Graph and Use Table3. Set Equations Equal4. Guess and Check

2.3 Comparing Costs

Step 6: Explain

How can this information be used to figure out which company to hire?

Explain why the relationship between the cost and the number of T-shirts for each company is a linear relationship.

2.3 Comparing Costs

Step 7: Compare a New Element

The table at the right represents the costs from another company, The Big T.

n C

0 34

3 41.5

5 46.5

8 54

10 59

2.3 Comparing Costs

1. Compare the Costs for this company with the costs for the other two companies.

2. Does this plan represent a linear relationship? Explain.

3. Could the point (20,84) lie on the graph of this cost plan? Explain.

4. What information about the number of T-shirts and cost do the coordinates of the point (20,84) represent?

2.4 Connecting Tables, Graphs, and Equations

Plan 1y = 5x – 3

Plan 2y = -x + 6

Plan 3y = 2

1.Does each plan make sense?

2.Make a table for values of x -5 to 5.

3.Sketch a graph

4.Do the y-values increase, decrease, or stay the same as the x-values increase?

2.4 Connecting Tables, Graphs, and Equations

1. Which graph can be traced to locate point (2,4)?

2. Which equation has a graph you can trace to find the value of x that makes 8 = 5x – 3 a true statement?

2.4 Connecting Tables, Graphs, and Equations

• The following three points all lie on the same plan.

(-7, 13) (1.2, y) (x, -4)

Which line are these points on?Find the missing coordinates.

Real Life Walkathon Project

1. Go out to the track and walk a mile. (4 laps)2. When you finish get your time from Ms. G.3. When you come inside, record your time and

find your walking rate.4. Make a table for time and distance.5. Make an equation for your table.6. Graph your data.7. Compare with your partner and find your point

of intersection.