Calculus Examples

$(7, 5)$ , $(- 3, 5)$

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.

$m = \frac{5 - (5)}{- 3 - (7)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $5$ .

$m = \frac{5 - 5}{- 3 - (7)}$

Step 4.1.2

Subtract $5$ from $5$ .

$m = \frac{0}{- 3 - (7)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $7$ .

$m = \frac{0}{- 3 - 7}$

Step 4.2.2

Subtract $7$ from $- 3$ .

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

Step 4.3

Divide $0$ by $- 10$ .

$m = 0$

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

The slope of the perpendicular line is $- \frac{1}{0}$ .

$m_{perpendicular} = - \frac{1}{0}$

Step 7

The slope of a line perpendicular to a horizontal line is undefined.

Undefined Slope

Step 8