Trigonometry Examples

$(- 1, 3)$ , $(2, 4)$

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.

$m = \frac{4 - (3)}{2 - (- 1)}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Multiply $- 1$ by $3$ .

$m = \frac{4 - 3}{2 - (- 1)}$

Step 4.1.2

Subtract $3$ from $4$ .

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

Step 4.2

Simplify the denominator.

Tap for more steps...

Step 4.2.1

Multiply $- 1$ by $- 1$ .

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

Step 4.2.2

Add $2$ and $1$ .

$m = \frac{1}{3}$

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 $- \frac{1}{\frac{1}{3}}$ .

Tap for more steps...

Step 6.1

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 \cdot 3)$

Step 6.2

Multiply $- (1 \cdot 3)$ .

Tap for more steps...

Step 6.2.1

Multiply $3$ by $1$ .

$m_{perpendicular} = - 1 \cdot 3$

Step 6.2.2

Multiply $- 1$ by $3$ .

$m_{perpendicular} = - 3$

Step 7