Algebra ( Period 5)

Chapter 3-2 Solving Linear Equations by Graphing

We need LOTS of graph paper. YOU must graph on graph paper—using a ruler or a straight edge! Make sure to label your x and y axes!  Put arrows on them!

Linear function: A line in the format:

f(x) = x or y = x

This is called the PARENT GRAPH

This parent graph has a FAMILY of GRAPHS related to it that has similar characteristics but is in someway different 
The Slope is Different
The y intercept is Different

The ROOT of the function or line is the X – intercept of the graph  It is called a ZERO on the graphing calculators. To find the root, find the value of x that makes the equation true when the y value is 0.

Linear functions ( equations) have at most 1  ROOT ( solution) because once the line intercepts the  x-axis it cannot curve around and intercept it again

Again, the FUNCTION is the ENTIRE GRAPH … and is in the form f(x) = x   or y = x

The linear EQUATION related to the function is only concerned with one value, the x- intercept.  The y value would be ZERO on the x-axis so you set the function = 0 and solve!

Here are the synonyms:
x-intercept= the solution = the root = the zero

 If you graph the function
f(x) = 2x – 8, you will see the x intercept is ( 4, 0)

Therefore, the solution, the root, the zero of the function is 4.

set f(x)  or y = 0
2x – 8 = 0
2x = 8
x = 4

You can solve a linear function 2 ways:

Graphically- Graph the function and read the x-intercept
Algebraically- Set y or f(x) equal to 0 and solve for x

Notice you are solving multi-step equation but now the value means that you found the root of the function. How often will you be able to read the exact answer from a graph? NOT OFTEN!

Therefore we usually solve for the root Algebraically!

Example:
Find the root or zero of y = 20- .75x

set y = 0

0 = 20 - .75x

x = 26 2/3