# Precalculus Examples

Find the Equation Using Two Points
,
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 m.
Simplify the numerator.
Multiply by to get .
Subtract from to get .
Simplify the denominator.
Remove parentheses.
Multiply by to get .
Move the negative in front of the fraction.
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 .
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 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 subtracting from 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 .
Multiply by to get .
Now that the values of (slope) and (y-intercept) are known, substitute them into to find the equation of the line.

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