Writing Equations in Standard Form

We know that equations can be written in slope intercept form or standard form.

Let's quickly revisit standard form. Remember standard form is written:

Ax +By= C

We can pretty easily translate an equation from slope intercept form into standard form. Let's look at an example.


Example 1: Rewriting Equations in Standard Form

Rewrite y = 2x - 6 in standard form.


Standard Form:  Ax + By = C

This means  that we want the variables (x & y) to be on the left-hand side and the constant (6) to be on the right-hand side.

When we move terms around, we do so exactly as we do when we solve equations!  So, remember... Whatever you do to one side of the equation, you must do to the other side!


Solution

Rewriting equations in standard form

That was a pretty easy example. We just need to remember that our lead coefficient should be POSITIVE!

Let's take a look at another example that involves fractions. There is one other rule that we must abide by when writing equations in standard form.


Equations that are written in standard form:

Ax + By = C

CANNOT contain fractions or decimals! A, B, and C MUST be integers!

Let's take a look at an example.


Example 2: Standard Form Equations

Rewrite y = 1/2x + 4 in standard form.


We now know that standard form equations should not contain fractions. Therefore, let's first eliminate the fractions.

Since the only fraction is is 1/2, we can multiply all terms by the denominator (2) to eliminate the fraction.


Solution

Writing Standard Form Equations

Now, let's look at an example that contains more than one fraction with different denominators.

Need More Help?

If you find that you need more examples or more practice problems, check out the Algebra Class E-course. You'll find additional examples on video, lots of practice problems with detailed solutions and little "tips" to help you through!


Example 3: Eliminating Fractions

Rewrite y = 3/4x - 1/8 in standard form.


Our first step is to eliminate the fractions, but this becomes a little more difficult when the fractions have different denominators!

We need to find the least common multiple (LCM) for the two fractions and then multiply all terms by that number!


Solution

Rewriting equations in standard form

Slope intercept form is the more popular of the two forms for writing equations. However, you must be able to rewrite equations in both forms.

For standard form equations, just remember that the A, B, and C must be integers and A should not be negative.


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