Slope Intercept to Standard Form

How to convert from y = mx + b to Ax + By = C

It is a common to ask to have to convert equation of line from slope intercept to standard form, as demonstrated by the pictures below.

General Formula Slope Intercept Form

Example

of Converting from Slope Intercept to Standard Form

Example

Convert , graphed on the right, to standard form.

Diagram of slope intercept form of line
Step 1

Multiply by the least common denominator of the fractions (if any)

The only fraction is so you can multiply everything by 4.

Step 2

Move" y1 to the other side by adding its opposite to both sides of the equation and simplify

Solve for the y-intercept (or "b" in the slope intercept equation) which is 20 in this example.

Practice Problems

Problem 1

Convert the the equation below from slope intercept form to standard form

Step 1

Multiply by the least common denominator of the fractions

The only fraction is so you can multiply everything by 3.

Step 2

Solve for the y-intercept (or "b" in the slope intercept equation) which is 12 in this problem.

Problem 2

Change the the equation below from slope intercept to standard from

Step 1

Multiply by the least common denominator of the fractions (if any)

The only fraction is so you can multiply everything by 2.

Step 2

Solve for the y-intercept (or "b" in the slope intercept equation) which is 10 in this problem.

Problem 3

Convert the the equation below from slope intercept to standard from

Step 1

Multiply all terms by the least common denominator of the fractions

Unlike the prior examples, this problem has two fractions so you can multiply everything by their common denominator of 9.

Step 2

Solve for the y-intercept (or "b" in the slope intercept equation) which, in this example, is 5.

Prroblem 4

Convert the the equation below from slope intercept to standard from

Step 1

Multiply all terms by the least common denominator of the fractions

This problem only has the fraction so we must multiply everything by 7.

Step 2

Solve for the y-intercept (or "b" in the slope intercept equation) which, in this example, is 4.

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Problem 5

Convert the the equation below from slope intercept to standard from (yes, this is a very challenging problem so let's see how sharp your algebra skills are.)

Step 1

Multiply all terms by the least common denominator of the fractions

This problem only has the fraction so we must multiply everything by c.

Step 2

Solve for the y-intercept (or "b" in the slope intercept equation) which, in this example, is the variable 'b'.