1. 6-3: Applying Linear Functions
Essential Question: What are some facts that you can find out about a real-world situation from reading a graph that models a situation.

2. 6-3: Applying Linear Functions
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

3. 6-3: Applying Linear Functions
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 = x

4. 6-3: Applying Linear Functions
Example 1 (continued)
y = x
Let’s reorder the right side… y = 6x + 40
Start with the y-intercept
b = 40
Use rise/run to make successive points
Up 6, over 1
Discrete points (not a line)
We’re counting # of car carriers

5. 6-3: Applying Linear Functions
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

6. 6-3: Applying Linear Functions
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 slope and y-intercept of graph mean for the given situation?
y-intercept is $25
Slope is 3
It means the class charged $3/car, and started with $25 in their account.

7. 6-3: Applying Linear Functions
If the graph had the same slope, but a y-intercept of 15, what would that mean?
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.

8. 6-3: Applying Linear Functions
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

9. 6-3: Applying Linear Functions
Assignment
Worksheet #6-3
All problems