Find the Slope (-2,-1) , (8,-3)

$(- 2, - 1)$ , $(8, - 3)$

Step 1

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

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

Step 2

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).

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

Step 3

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

$m = \frac{- 3 - (- 1)}{8 - (- 2)}$

Step 4

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 1$ .

$m = \frac{- 3 + 1}{8 - (- 2)}$

Add $- 3$ and $1$ .

$m = \frac{- 2}{8 - (- 2)}$

Simplify the denominator.

Multiply $- 1$ by $- 2$ .

$m = \frac{- 2}{8 + 2}$

Add $8$ and $2$ .

$m = \frac{- 2}{10}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 2$ and $10$ .

Factor $2$ out of $- 2$ .

$m = \frac{2 (- 1)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$m = \frac{2 \cdot - 1}{2 \cdot 5}$

Cancel the common factor.

$m = \frac{2 \cdot - 1}{2 \cdot 5}$

Rewrite the expression.

$m = \frac{- 1}{5}$

Move the negative in front of the fraction.

$m = - \frac{1}{5}$

Step 5

Find the Slope (-2,-1) , (8,-3)

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