# Algebra 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.
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 .
Rewrite.
Write as a fraction with denominator .
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Simplify.
Multiply by to get .
Multiply and to get .
Multiply by to get .
Divide by to get .
Cancel the common factor of .
Rewrite.
Write as a fraction with denominator .
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Rewrite the expression.
Simplify.
Multiply and to get .
Multiply by to get .
Divide by to get .
Simplify the numerator.
Multiply by to get .
Subtract from to get .
Simplify the denominator.
Rewrite.
Apply the distributive property.
Cancel the common factor of .
Reduce the expression by cancelling the common factors.
Simplify.
Multiply by to get .
Subtract from to get .
Reduce the expression by cancelling the common factors.
Reduce the expression by cancelling the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
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 and to get .
Multiply by to get .
Reduce the expression by cancelling the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
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 adding to both sides.
Simplify the right side of the equation.
Combine the numerators over the common denominator.
Add and 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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