1. Linear Functions
Students will be able to determine whether or not a function is linear and be able to write a linear function given a real world situation.

2. Linear Functions
When given a data set, we can determine whether it is a linear or nonlinear function.
We look at the rate of change. This is found by dividing the change in the y or f(x) by the change in the x.
If the rate of change is constant, then the function is linear.
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Functions

3. Data Sets We need to find the change in f(x) and the change in x.
___ ___ ___ ___ x -2 -1 1 2
y or f(x) -5 4 7
____ ____ ____ ____
The ratio is constant, so this is linear.
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Functions

4. Slope of a Line
The ratio that represents the rate of change is also called the slope of the line.
A set of data that has a constant rate of change is a linear function. The slope of that line is the rate and the function can be graphed using those points and the slope of the line.
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Functions

5. Solving Problems
We can use this information about linear functions to help us solve problems. For example:
Joe sells tents at the Outdoor Store. He is paid $56 a day and gets a $10 commission on every tent he sells. Write an equation that represents this, and compute Joe’s salary for a day if he sells 3 tents.
x would represent the number of tents sold
y would represent Joe’s daily salary.
The equation would be:
So Joe’s salary would be:
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Functions