You have learned many techniques for graphing linear equations that are written in slope intercept form! Yes... if the equation is already written in slope intercept form, graphing is pretty easy!

However, sometimes you will see equations that are written in standard form.

What is Standard Form?

Standard Form is presented as:

Ax + By = C

Where A and B are coefficients and C is a constant.

Examples: 2x + 4y = 8 5x - 7y = 12 3x - 9y = -18

If the equation is presented in standard form, then you are not able
to identify the slope and y-intercept that are needed for graphing.

So... what should you do?

There are actually two different techniques that you can use for
graphing linear equations that are written in standard form. You can
use either method, so I'm going to demonstrate both methods and you may
come to favor one over the other.

In this particular lesson, we are going to study how to convert the
standard form equation into an equation written in slope intercept form.

In the next lesson, we will study a method using x and y intercepts

Let's get started! If you have a standard form equation, you can
rewrite it in slope intercept form. Let's look at a couple of examples.

Example 1: Rewriting an Equation in Slope Intercept Form

Your goal when rewriting a standard form equation in slope intercept form is to rewrite the equation so that it reads y = mx + b.

You will need to use your knowledge of solving equations.

Remember to use opposite operations and whatever you do to one side of the equation, you must do to the other side.

Let's rewrite 4x - 6y = 12 in slope intercept form so that we can easily graph the equation.

For a step by step video on rewriting this standard form equation in slope intercept form, watch the following video:

Notice how graphing is pretty easy once it's written in slope
intercept form. Standard form equations can always be rewritten in
slope intercept form. Make sure you solve the equation for y, and
that's it!

Let's look at one more example.

Example 2: Rewriting Standard Form Equations in Slope Intercept Form

Graph the equation 2x + 8y = -24.

This shouldn't be too hard, since you've already mastered the skills
for solving equations and the skills for graphing in slope intercept
form.

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