# Algebra Examples

,

Step 1

Step 1.1

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

Step 1.2

Using the slope-intercept form, the slope is .

Step 2

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

Step 3

Step 3.1

Move the negative in front of the fraction.

Step 3.2

Multiply .

Step 3.2.1

Multiply by .

Step 3.2.2

Multiply by .

Step 4

Step 4.1

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

Step 4.2

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

Step 5

Step 5.1

Solve for .

Step 5.1.1

Simplify .

Step 5.1.1.1

Rewrite.

Step 5.1.1.2

Simplify by adding zeros.

Step 5.1.1.3

Apply the distributive property.

Step 5.1.1.4

Combine and .

Step 5.1.1.5

Combine and .

Step 5.1.2

Move all terms not containing to the right side of the equation.

Step 5.1.2.1

Subtract from both sides of the equation.

Step 5.1.2.2

To write as a fraction with a common denominator, multiply by .

Step 5.1.2.3

Combine and .

Step 5.1.2.4

Combine the numerators over the common denominator.

Step 5.1.2.5

Simplify the numerator.

Step 5.1.2.5.1

Multiply by .

Step 5.1.2.5.2

Subtract from .

Step 5.1.2.6

Move the negative in front of the fraction.

Step 5.2

Reorder terms.

Step 6