# Precalculus Examples

,

Slope is equal to the change in over the change in , or rise over run.

The change in is equal to the difference in x-coordinates (also called run), and the change in is equal to the difference in y-coordinates (also called rise).

Substitute in the values of and into the equation to find the slope.

Simplify.

Simplify the numerator.

Multiply by .

Subtract from .

Simplify the denominator.

Remove parentheses.

Multiply by .

Add and .

Move the negative in front of the fraction.

Use the slope and one of the given points such as to substitute for and in the point-slope form , which is derived from the slope equation .

After finding the slope between the points, use point-slope form to set up the equation. Point-slope is derived from the equation for slope .

Multiply by .

Simplify the right side.

Simplify the expression.

Multiply by .

Apply the distributive property.

Simplify .

Write as a fraction with denominator .

Multiply and .

Simplify .

Multiply by .

Write as a fraction with denominator .

Multiply and .

Multiply by .

Simplify each term.

Move to the left of the expression .

Multiply by .

Move the negative in front of the fraction.

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

Add to both sides of the equation.

Simplify the right side of the equation.

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Multiply by .

Subtract from .

The final answer is the equation in slope-intercept form.