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

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

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.

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

Step 4

Simplify.

Reduce the expression by cancelling the common factors.

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

Rewrite $3$ as $- 1 (- 3)$ .

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

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

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

Reorder terms.

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

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

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

Cancel the common factors.

Factor $3$ out of $6$ .

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

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Subtract $1$ from $- 1$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

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

Add $2$ and $1$ .

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

Multiply $- 1$ by $- 2$ .

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

Step 5

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

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