A compiled group of resources that will help you learn all about linear equations. Some of these you will have seen through the class website, but I wanted you to have access to all of the information in one location.

SLOPE

CHARACTERISTICS OF SLOPE

This is an example of POSITIVE SLOPE. Notice that the bird is going up the line.

This is an example of NEGATIVE SLOPE. Notice the bird is going down the line.

This is an example of ZERO SLOPE. Notice the bird is moving in along a horizontal line.

This is an example of UNDEFINED SLOPE. Notice the bird is falling along a vertical line.

FINDING SLOPE FROM A GRAPH

FINDING SLOPE USING SLOPE FORMULA

We use the Slope Formula to find the slope between two given points. These may or may not be on a graph, so it is important that you understand the relationship between the rise divided by the run, or the change in y-values divided by the change in x-values. Regardless on how you think about slope, the formula above is the simplified version of that thought. The key to USING this formula is to label your points properly BEFORE you plug numbers into the equation. What the video below for a proper example of labeling and solving for the slope when given two points.

FINDING SLOPE FROM TWO POINTS

Slope-Intercept Form

The Slope-Intercept Form is the traditional equation we will use to represent linear functions. In this equation, we can quickly identify the slope (represented by the m) and the y-intercept (represented by the b). This allows us to graph equations quickly, and determine certain aspects of the function.

WRITE EQUATION IN SLOPE-INTERCEPT FORM

GRAPH A LINE GIVEN SLOPE AND Y-INTERCEPT (from slope-intercept form)

Standard Form

The Standard Form is a different way we can write a linear function. Often we will convert equations out of Standard Form into Slope-Intercept Form. The information we gather from view the slope and y-intercept is very valuable in Algebra. The link below will walk you through how to complete this conversion.

Several key features of this equation exist. One, the X-variable and the Y-variable are on the same side of the equation. Two, the constant in from of the X-Variable (denoted by A in the equation) cannot be negative, and must be a whole number. Three, we can quickly identify the intercepts using this equation.

SIDE NOTE: The spaces represented by A, B, and C are just constants or numbers.  THEY ARE NOT VARIABLES.

CONVERT STANDARD FORM INTO SLOPE-INTERCEPT FORM

GRAPH A LINE USING X-INTERCEPT AND Y-INTERCEPT

Point-Slope Formula

The point-slope formula is another method that we use to write a linear equation. You may use this equation when you are given a single point (which may or may not be the y-intercept) OR when you are given two points. Once we have the information substituted into the point-slope formula, you will traditionally be asked to convert this equation into the slope-intercept form.

WRITING AN EQUATION IN POINT-SLOPE FORM GIVEN A POINT & SLOPE

WRITING AN EQUATION IN POINT-SLOPE FORM GIVEN TWO POINTS

CONVERTING POINT-SLOPE FORM TO SLOPE-INTERCEPT FORM

Vertical & Horizontal Lines

VERTICAL LINES

A vertical line is written in the form x=a, where a is the x-intercept of the line.

GRAPH VERTICAL LINES

WRITE EQUATIONS FOR VERTICAL LINES

HORIZONTAL LINES

A horizontal line is written in the form y=b, where b is the y-intercept of the line.

GRAPH HORIZONTAL LINES

WRITE EQUATION FOR HORIZONTAL LINES