Find the Slope (-3,5) , (6,2)

$(- 3, 5)$ , $(6, 2)$

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.

$m = \frac{2 - (5)}{6 - (- 3)}$

Step 4

Simplify.

Simplify the numerator.

Multiply $- 1$ by $5$ .

$m = \frac{2 - 5}{6 - (- 3)}$

Subtract $5$ from $2$ .

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

Simplify the denominator.

Multiply $- 1$ by $- 3$ .

$m = \frac{- 3}{6 + 3}$

Add $6$ and $3$ .

$m = \frac{- 3}{9}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 3$ and $9$ .

Factor $3$ out of $- 3$ .

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

Cancel the common factors.

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 5

Find the Slope (-3,5) , (6,2)

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