Find the Slope (1,-1) , (5,-7)

$(1, - 1)$ , $(5, - 7)$

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.

$m = \frac{- 7 - (- 1)}{5 - (1)}$

Step 4

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 1$ .

$m = \frac{- 7 + 1}{5 - (1)}$

Add $- 7$ and $1$ .

$m = \frac{- 6}{5 - (1)}$

Simplify the denominator.

Multiply $- 1$ by $1$ .

$m = \frac{- 6}{5 - 1}$

Subtract $1$ from $5$ .

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 6$ and $4$ .

Factor $2$ out of $- 6$ .

$m = \frac{2 (- 3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 5

Find the Slope (1,-1) , (5,-7)

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