Algebra Examples

$(2, 7)$ , $(3, 3)$

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{3 - (7)}{3 - (2)}$

Simplify.

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Simplify the numerator.

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Multiply $- 1$ by $7$ to get $- 7$ .

$m = \frac{3 - 7}{3 - (2)}$

Subtract $7$ from $3$ to get $- 4$ .

$m = \frac{- 4}{3 - (2)}$

Simplify the denominator.

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Remove parentheses.

$m = \frac{- 4}{3 - (2)}$

Multiply $- 1$ by $2$ to get $- 2$ .

$m = \frac{- 4}{3 - 2}$

Subtract $2$ from $3$ to get $1$ .

$m = \frac{- 4}{1}$

Divide $- 4$ by $1$ to get $- 4$ .

$m = - 4$

The slope of a perpendicular line is the negative reciprocal of the slope of the line that passes through the two given points.

$m_{perpendicular} = - \frac{1}{m}$

Simplify $- \frac{1}{- 4}$ .

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Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{4}$

Simplify $- - \frac{1}{4}$ .

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Multiply $- 1$ by $- 1$ to get $1$ .

$m_{perpendicular} = 1 (\frac{1}{4})$

Multiply $\frac{1}{4}$ by $1$ to get $\frac{1}{4}$ .

$m_{perpendicular} = \frac{1}{4}$

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