how can you solve a problem using a linear relationship if you are not given an initial value?

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How can you solve a problem using a linear relationship if you are not given an initial value?

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How can you solve a problem using a linear relationship if you are not given an initial value?. In this lesson you will learn how to solve a problem involving a linear relationship by making a table and graph. - PowerPoint PPT Presentation

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Page 1: How can you solve a problem using a linear relationship if you are not given an initial value?

How can you solve a problem using a linear relationship if you are not given an initial

value?

Page 2: How can you solve a problem using a linear relationship if you are not given an initial value?

In this lesson you will learn how to solve a problem

involving a linear relationship by making a table and graph.

Page 3: How can you solve a problem using a linear relationship if you are not given an initial value?

Let’s Review

Linear relationships are commonly expressed in three ways: tables,

graphs, and equations.

x y

-3 -4

0 -2

3 0

6 2

y = mx + b

+3

+2

+2

+2

+3

+3

Page 4: How can you solve a problem using a linear relationship if you are not given an initial value?

A Common Mistake

Interpreting the wrong point as the y-intercept

Page 5: How can you solve a problem using a linear relationship if you are not given an initial value?

Core Lesson

You are going to a carnival with your friend. You know that there is a fee to get into the carnival, and then you also

pay to go on rides.Your friend paid $5.50 and rode 2 rides.

Each ride costs $0.75.

How much will it cost to pay the entry fee and ride 8 rides?

Constant rate of change

Page 6: How can you solve a problem using a linear relationship if you are not given an initial value?

Core Lesson

Number of Rides Cost

0 ??

1 ??

2 $5.50

3 $6.25

4 $7.00

5 $7.75

+0.75

+0.75

+0.75

Rate of change = slope = $0.75

Page 7: How can you solve a problem using a linear relationship if you are not given an initial value?

Core Lesson

How to solve this problem?

1) Use the table2) Find an equation to model this

function3) Put the points from the table on a

graph, and use the graph

Page 8: How can you solve a problem using a linear relationship if you are not given an initial value?

Core Lesson

Number of Rides Cost

0

1

2 $5.50

3 $6.25

4 $7.00

5 $7.75

6 $8.50

7 $9.25

8 $10.00

+0.75

+0.75

+0.75

Page 9: How can you solve a problem using a linear relationship if you are not given an initial value?

Core Lesson

How to solve this problem?

1) Use the table2) Find an equation to model this

function3) Put the points from the table on a

graph, and use the graph

Page 10: How can you solve a problem using a linear relationship if you are not given an initial value?

Core Lesson

Number of Rides Cost

0

1

2 $5.50

3 $6.25

4 $7.00

5 $7.75

c = $0.75r + $4.00

$4.75

$4.00

c = $0.75(8) + $4.00 = $10.00

-0.75

-0.75

Work backwards

Page 11: How can you solve a problem using a linear relationship if you are not given an initial value?

Core Lesson

How to solve this problem?

1) Use the table2) Find an equation to model this

function3) Put the points from the table on a

graph, and use the graph

Page 12: How can you solve a problem using a linear relationship if you are not given an initial value?

Core Lesson

Number of Rides Cost

0

1

2 $5.50

3 $6.25

4 $7.00

5 $7.75

+0.75

+0.75

+0.75

Rate of change = slope = $0.75 = ¾

Page 13: How can you solve a problem using a linear relationship if you are not given an initial value?

Core Lesson

Number of rides

Cost (in dollars)

(4, $7.00)(5, $7.75)

(3, $6.25)(2, $5.50)

(8, $10.00)

Page 14: How can you solve a problem using a linear relationship if you are not given an initial value?

In this lesson you have learned how to solve a problem

involving a linear relationship by making a table and

graphing.

Page 15: How can you solve a problem using a linear relationship if you are not given an initial value?

Guided Practice

A 2-mile cab ride costs $5.25. A 5-mile cab ride costs $10.50. How much does a 4.2-mile cab ride cost, if the cost of the cab is calculated by the mile?

Page 16: How can you solve a problem using a linear relationship if you are not given an initial value?

Extension Activities

Page 17: How can you solve a problem using a linear relationship if you are not given an initial value?

Extension Activities

Page 18: How can you solve a problem using a linear relationship if you are not given an initial value?

Quick Quiz

A water jug with 3 cups of water in it weighs 2.25 pounds. With 5 cups of water it weighs 3.25 pounds. How much does the water jug weigh when empty?

Page 19: How can you solve a problem using a linear relationship if you are not given an initial value?

Quick Quiz

Sean likes to eat cookies. He eats 3 cookies per day. Five days after opening a box of cookies, there are 24 cookies left in the box. How many cookies were in the box at the time it was opened?