Find the Slope (-4,7) , (2,-8)

$(- 4, 7)$ , $(2, - 8)$

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.

$m = \frac{- 8 - (7)}{2 - (- 4)}$

Step 4

Simplify.

Simplify the numerator.

Multiply $- 1$ by $7$ .

$m = \frac{- 8 - 7}{2 - (- 4)}$

Subtract $7$ from $- 8$ .

$m = \frac{- 15}{2 - (- 4)}$

Simplify the denominator.

Multiply $- 1$ by $- 4$ .

$m = \frac{- 15}{2 + 4}$

Add $2$ and $4$ .

$m = \frac{- 15}{6}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 15$ and $6$ .

Factor $3$ out of $- 15$ .

$m = \frac{3 (- 5)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$m = \frac{3 \cdot - 5}{3 \cdot 2}$

Cancel the common factor.

$m = \frac{3 \cdot - 5}{3 \cdot 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 5

Find the Slope (-4,7) , (2,-8)

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