3.2 Zeros of Linear Functions

3.2 Zeros of Linear Functions

Make sure to have a piece of paper and a pencil!

Linear Function

• The graph is a line

• Parent function is the simplest version: $f\left(x\right)=x\ or\ y=x$  

• The parent then has a family that all look like it (a straight line)

Solution of the Equation

• Also called the root or the zero

• On a graph, it's also called the x-intercept

• Makes the equation true

• This is the graph:

   $y=2x+4$  

• So: the solution is -2

Open Ended

What is the solution to the following equation:

 $0=-0.5x+2$  

This graph does not have an x-intercept

- The answer to a graph like this is no solutions

Solving without a Graph

• If have just the equation, you can also solve it by solving for x

• Ex: $0=3x+6$  

Open Ended

Without graphing, what is the solution to the following equation:

 $0=2x+8$  

Now It's Your Turn!

The following five questions will be graded as an assignment.

Open Ended

Using the graph, determine the solution of

 $0=-4x+4$  

Open Ended

Using the graph, determine the solution of

 $0=x+3$  

Open Ended

Without graphing, what is the solution to the following equation:

 $0=4x-16$  

Open Ended

Using the graph, what is the solution of

 $0=6x+12$  

Open Ended

Without graphing, what is the solution of

 $0=3x-21$