Find the Slope (4,-2) , (-5,4)

$(4, - 2)$ , $(- 5, 4)$

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.

$m = \frac{4 - (- 2)}{- 5 - (4)}$

Step 4

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 2$ .

$m = \frac{4 + 2}{- 5 - (4)}$

Add $4$ and $2$ .

$m = \frac{6}{- 5 - (4)}$

Simplify the denominator.

Multiply $- 1$ by $4$ .

$m = \frac{6}{- 5 - 4}$

Subtract $4$ from $- 5$ .

$m = \frac{6}{- 9}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $6$ and $- 9$ .

Factor $3$ out of $6$ .

$m = \frac{3 (2)}{- 9}$

Cancel the common factors.

Factor $3$ out of $- 9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 5

Find the Slope (4,-2) , (-5,4)

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