Algebra Examples

$(- 10, 1)$ , $(0, - 4)$

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.

$m = \frac{- 4 - (1)}{0 - (- 10)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $1$ .

$m = \frac{- 4 - 1}{0 - (- 10)}$

Step 4.1.2

Subtract $1$ from $- 4$ .

$m = \frac{- 5}{0 - (- 10)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $- 10$ .

$m = \frac{- 5}{0 + 10}$

Step 4.2.2

Add $0$ and $10$ .

$m = \frac{- 5}{10}$

Step 4.3

Reduce the expression by cancelling the common factors.

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Step 4.3.1

Cancel the common factor of $- 5$ and $10$ .

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Step 4.3.1.1

Factor $5$ out of $- 5$ .

$m = \frac{5 (- 1)}{10}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $5$ out of $10$ .

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

Step 4.3.1.2.2

Cancel the common factor.

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

Step 4.3.1.2.3

Rewrite the expression.

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

Step 4.3.2

Move the negative in front of the fraction.

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

Step 5