,

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 .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Move the leading negative in into the numerator.

Cancel the common factor.

Rewrite the expression.

Simplify the numerator.

Multiply by .

Multiply .

Multiply by .

Multiply by .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Add and .

Simplify the expression.

Subtract from .

Divide by .

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 .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

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

Subtract from both sides of the equation.

Subtract from .

Combine and .

Move the negative in front of the fraction.

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

Find the Equation Using Two Points (1/6,-1/3) , (5/6,1)