Guidelines for Graphing

Finding the Slope of a Line

Slope

The slope of a line measures the steepness of the line.

Most of you are probably familiar with associating slope with "rise over run".

Rise means how many units you move up or down from point to point. On the graph that would be a change in the y values.

Run means how far left or right you move from point to point. On the graph, that would mean a change of x values.

Here are some visuals to help you with this definition:

Positive slope:

Note that when a line has a positive slope it goes up left to right.

Negative slope:

Note that when a line has a negative slope it goes down left to right.

Zero slope:

slope = 0

Note that when a line is horizontal the slope is 0.

Undefined slope:

slope = undefined

Note that when the line is vertical the slope is undefined.

Slope Formula Given Two Points

Given two points and

The subscripts just indicate that these are two different points. It doesn't matter which one you call point 1 and which one you call point 2 as long as you are consistent throughout that problem.

Note that we use the letter m to represent slope.

Slope/Intercept Equation of a Line

If your linear equation is written in this form, m represents the slope and b represents the y-intercept.

This form can be handy if you need to find the slope of a line given the equation.

Function Notation of the
Slope/Intercept Equation of a Line

m still represents slope and b still represents the y-intercept.

Practice Problem:

Determine the slope of the line.

(answer/discussion to Example Problem)