# Algebra Examples

,

Use to calculate the equation of the line, where represents the slope and represents the y-intercept.

To calculate the equation of the line, use the format.

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.

Multiply the numerator and denominator of the complex fraction by .

Multiply by .

Combine.

Apply the distributive property.

Simplify by cancelling.

Cancel the common factor of .

Move the leading negative in into the numerator.

Write as a fraction with denominator .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Simplify.

Multiply and .

Multiply by .

Divide by .

Cancel the common factor of .

Move the leading negative in into the numerator.

Write as a fraction with denominator .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Simplify.

Multiply and .

Multiply by .

Divide by .

Simplify the numerator.

Multiply by .

Subtract from .

Simplify the denominator.

Multiply by .

Subtract from .

Reduce the expression by cancelling the common factors.

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Use the formula for the equation of a line to find .

Substitute the value of into the equation.

Substitute the value of into the equation.

Substitute the value of into the equation.

Find the value of .

Rewrite the equation as .

Simplify each term.

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Simplify.

Multiply and .

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.

Combine the numerators over the common denominator.

Add and .

Now that the values of (slope) and (y-intercept) are known, substitute them into to find the equation of the line.