Basic Math Examples

$(4, 4)$ , $(3, 4)$

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.

$m = \frac{4 - (4)}{3 - (4)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $4$ .

$m = \frac{4 - 4}{3 - (4)}$

Step 4.1.2

Subtract $4$ from $4$ .

$m = \frac{0}{3 - (4)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $4$ .

$m = \frac{0}{3 - 4}$

Step 4.2.2

Subtract $4$ from $3$ .

$m = \frac{0}{- 1}$

Step 4.3

Divide $0$ by $- 1$ .

$m = 0$

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