Find the Slope (6,-6) , (2,-6)

$(6, - 6)$ , $(2, - 6)$

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.

$m = \frac{- 6 - (- 6)}{2 - (6)}$

Step 4

Simplify.

Cancel the common factor of $- 6 - (- 6)$ and $2 - (6)$ .

Rewrite $2$ as $- 1 (- 2)$ .

$m = \frac{- 6 - (- 6)}{- 1 \cdot - 2 - (6)}$

Factor $- 1$ out of $- 1 (- 2) - (6)$ .

$m = \frac{- 6 - (- 6)}{- 1 (- 2 + 6)}$

Reorder terms.

$m = \frac{- 6 - 6 \cdot - 1}{- 1 (- 2 + 6)}$

Factor $2$ out of $- 6$ .

$m = \frac{2 (- 3) - 6 \cdot - 1}{- 1 (- 2 + 6)}$

Factor $2$ out of $- 6 \cdot - 1$ .

$m = \frac{2 (- 3) + 2 (- 3 \cdot - 1)}{- 1 (- 2 + 6)}$

Factor $2$ out of $2 (- 3) + 2 (- 3 \cdot - 1)$ .

$m = \frac{2 (- 3 - 3 \cdot - 1)}{- 1 (- 2 + 6)}$

Cancel the common factors.

Factor $2$ out of $- 1 (- 2 + 6)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

Multiply $- 3$ by $- 1$ .

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

Add $- 3$ and $3$ .

$m = \frac{0}{- 1 (- 1 + 3)}$

Simplify the expression.

Add $- 1$ and $3$ .

$m = \frac{0}{- 1 \cdot 2}$

Multiply $- 1$ by $2$ .

$m = \frac{0}{- 2}$

Divide $0$ by $- 2$ .

$m = 0$

Step 5

Find the Slope (6,-6) , (2,-6)

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