,

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.

Simplify the numerator.

Multiply by .

Subtract from .

Simplify the denominator.

Multiply by .

Subtract from .

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.

Multiply .

Multiply by .

Combine and .

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.

Write as a fraction with a common denominator.

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.

Find the Equation Using Two Points (5,1) , (-2,3)