Calculus Examples

$(- 2, 2)$ , $(0, 7)$

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.

$m = \frac{7 - (2)}{0 - (- 2)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $2$ .

$m = \frac{7 - 2}{0 - (- 2)}$

Step 4.1.2

Subtract $2$ from $7$ .

$m = \frac{5}{0 - (- 2)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $- 2$ .

$m = \frac{5}{0 + 2}$

Step 4.2.2

Add $0$ and $2$ .

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

Step 5

The slope of a perpendicular line is the negative reciprocal of the slope of the line that passes through the two given points.

$m_{perpendicular} = - \frac{1}{m}$

Step 6

Simplify $- \frac{1}{\frac{5}{2}}$ .

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Step 6.1

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{2}{5}))$

Step 6.2

Multiply $\frac{2}{5}$ by $1$ .

$m_{perpendicular} = - \frac{2}{5}$

Step 7