# 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 to get .

Subtract from to get .

Simplify the denominator.

Remove parentheses.

Multiply by to get .

Subtract from to get .

Move the negative in front of the fraction.

Substitute the value of into the slope-intercept form of the equation, .

Substitute the value of into the slope-intercept form of the equation, .

Substitute the value of into the slope-intercept form of the equation, .

Rewrite the equation as .

Simplify each term.

Multiply by to get .

Simplify .

Multiply by to get .

Write as a fraction with denominator .

Multiply and to get .

Multiply by to get .

Move the negative in front of the fraction.

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

Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.

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 to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by to get .

Add and to get .

The values of the slope and y-intercept are and