# Find the Equation Using Two Points (1,-3) , (5,7)

,
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.
Finding the slope .
Simplify the numerator.
Multiply by .
Simplify the denominator.
Multiply by .
Subtract from .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Find the value of using the formula for the equation of a line.
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 .
Multiply by .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
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,-3) , (5,7)