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.
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
A Common Mistake
Interpreting the wrong point as the y-intercept
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
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
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
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
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
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
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
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
Core Lesson
Number of rides
Cost (in dollars)
(4, $7.00)(5, $7.75)
(3, $6.25)(2, $5.50)
(8, $10.00)
In this lesson you have learned how to solve a problem
involving a linear relationship by making a table and
graphing.
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?
Extension Activities
Extension Activities
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?
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?
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