# Algebra Examples

Step 1

Choose a point that the perpendicular line will pass through.

Step 2

Step 2.1

Subtract from both sides of the equation.

Step 2.2

Divide each term in by and simplify.

Step 2.2.1

Divide each term in by .

Step 2.2.2

Simplify the left side.

Step 2.2.2.1

Cancel the common factor of .

Step 2.2.2.1.1

Cancel the common factor.

Step 2.2.2.1.2

Divide by .

Step 2.2.3

Simplify the right side.

Step 2.2.3.1

Move the negative in front of the fraction.

Step 3

Step 3.1

Rewrite in slope-intercept form.

Step 3.1.1

The slope-intercept form is , where is the slope and is the y-intercept.

Step 3.1.2

Write in form.

Step 3.1.2.1

Reorder terms.

Step 3.1.2.2

Remove parentheses.

Step 3.2

Using the slope-intercept form, the slope is .

Step 4

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

Step 5

Step 5.1

Cancel the common factor of and .

Step 5.1.1

Rewrite as .

Step 5.1.2

Move the negative in front of the fraction.

Step 5.2

Multiply the numerator by the reciprocal of the denominator.

Step 5.3

Multiply by .

Step 5.4

Multiply .

Step 5.4.1

Multiply by .

Step 5.4.2

Multiply by .

Step 6

Step 6.1

Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .

Step 6.2

Simplify the equation and keep it in point-slope form.

Step 7

Step 7.1

Solve for .

Step 7.1.1

Add and .

Step 7.1.2

Simplify .

Step 7.1.2.1

Add and .

Step 7.1.2.2

Combine and .

Step 7.2

Reorder terms.

Step 8