Precalculus Examples

$(5, - 1)$ , $(- 2, 4)$

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.

$m = \frac{4 - (- 1)}{- 2 - (5)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $- 1$ .

$m = \frac{4 + 1}{- 2 - (5)}$

Step 4.1.2

Add $4$ and $1$ .

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

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $5$ .

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

Step 4.2.2

Subtract $5$ from $- 2$ .

$m = \frac{5}{- 7}$

Step 4.3

Move the negative in front of the fraction.

$m = - \frac{5}{7}$

Step 5