Find the Slope (-9,-6) , (3,-9)

$(- 9, - 6)$ , $(3, - 9)$

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.

$m = \frac{- 9 - (- 6)}{3 - (- 9)}$

Step 4

Simplify.

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 9 - (- 6)$ and $3 - (- 9)$ .

Rewrite $- 9$ as $- 1 (9)$ .

$m = \frac{- 1 \cdot 9 - (- 6)}{3 - (- 9)}$

Factor $- 1$ out of $- 1 (9) - (- 6)$ .

$m = \frac{- 1 (9 - 6)}{3 - (- 9)}$

Reorder terms.

$m = \frac{- 1 (9 - 6)}{3 - 9 \cdot - 1}$

Factor $3$ out of $- 1 (9 - 6)$ .

$m = \frac{3 (- 1 (3 - 2))}{3 - 9 \cdot - 1}$

Cancel the common factors.

Factor $3$ out of $3$ .

$m = \frac{3 (- 1 (3 - 2))}{3 (1) - 9 \cdot - 1}$

Factor $3$ out of $- 9 \cdot - 1$ .

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

Factor $3$ out of $3 (1) + 3 (- 3 \cdot - 1)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Subtract $2$ from $3$ .

$m = \frac{- 1 \cdot 1}{1 - 3 \cdot - 1}$

Simplify the denominator.

Multiply $- 3$ by $- 1$ .

$m = \frac{- 1 \cdot 1}{1 + 3}$

Add $1$ and $3$ .

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

Simplify the expression.

Multiply $- 1$ by $1$ .

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

Move the negative in front of the fraction.

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

Step 5

Find the Slope (-9,-6) , (3,-9)

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