Algebra Examples

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

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.

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

Step 4

Simplify.

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Step 4.1

Reduce the expression by cancelling the common factors.

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Step 4.1.1

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

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Step 4.1.1.1

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

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

Step 4.1.1.2

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

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

Step 4.1.1.3

Reorder terms.

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

Step 4.1.1.4

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

$m = \frac{3 (- 1 (3 + 2))}{- 6 - 9 \cdot - 1}$

Step 4.1.1.5

Cancel the common factors.

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Step 4.1.1.5.1

Factor $3$ out of $- 6$ .

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

Step 4.1.1.5.2

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

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

Step 4.1.1.5.3

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

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

Step 4.1.1.5.4

Cancel the common factor.

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

Step 4.1.1.5.5

Rewrite the expression.

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

Step 4.1.2

Add $3$ and $2$ .

$m = \frac{- 1 \cdot 5}{- 2 - 3 \cdot - 1}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 3$ by $- 1$ .

$m = \frac{- 1 \cdot 5}{- 2 + 3}$

Step 4.2.2

Add $- 2$ and $3$ .

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

Step 4.3

Simplify the expression.

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Step 4.3.1

Multiply $- 1$ by $5$ .

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

Step 4.3.2

Divide $- 5$ by $1$ .

$m = - 5$

Step 5