Essential Question: What are some facts that you can find out about a real-world situation

from reading a graph that models a situation.

You can model many real world situations with linear equations.

Remember that a graph of an equation shows the solutions of that equation

However, for discrete situations, not every point may represent a reasonable value.◦ Remember: Discrete Data is Counted◦ Continuous Data is Measured

Example 1◦ A car dealership has 40 cars in stock. The auto

manufacturer will deliver new cars to the dealership by car carrier. Each carrier holds 6 cars. Write a linear function that relates the number of carriers used to the total number of cars at the dealership. Graph the function that models the situation. The total equals 40 plus 6 times the number of

number of cars car carriers Let x = the number of car carriers

Let y = the total number of cars y = 40 + 6x

Example 1 (continued)◦ y = 40 + 6x◦ Let’s reorder the right side… y = 6x + 40

◦ Start with the y-intercept b = 40

◦ Use rise/run to makesuccessive points Up 6, over 1

◦ Discrete points (not a line) We’re counting # of car carriers

Your Turn◦ A sporting goods store sells cans of tennis balls.

There are 3 tennis balls in each can. Write a linear function that relates the number of cans to the total number of tennis balls. t = number of tennis balls

c = number of cans t = 3n

1 2 3 4 5 6 7 8 9 x

2

4

6

8

10

12

14

16

18

20y

Example 2: Analyzing Linear Graphs◦ Students in a ninth-grade class drew the following

graph to represent how much money would be in the class fund after washing cars at a fundraiser.

◦ What does the slopeand y-intercept ofgraph mean for thegiven situation? y-intercept is $25 Slope is 3 It means the class

charged $3/car, and started with $25 in their account.

If the graph had thesame slope, but ay-intercept of 15,what would thatmean?◦ It would mean that

the class started with$15 instead of $25

If the graph had a slope of 5, what could you conclude?◦ That the class charged $5/car instead of $3.

Your Turn◦ Suppose you drew the following graph to

represent how far you ride your bike at a steady rate.

◦ What is your rate? 12 miles/hr

◦ If the graph had a slope of 10, what could you conclude about your bike ride? Your rate would be 10 miles/hr

Assignment◦ Worksheet #6-3◦ All problems