Find the Slope of a Perpendicular Line y=5/7x+3

$y = \frac{5}{7} x + 3$

Step 1

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Simplify the right side.

Combine $\frac{5}{7}$ and $x$ .

$y = \frac{5 x}{7} + 3$

Reorder terms.

$y = \frac{5}{7} x + 3$

Step 2

Using the slope-intercept form, the slope is $\frac{5}{7}$ .

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

Step 3

The equation of a perpendicular line to $y = \frac{5}{7} x + 3$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{\frac{5}{7}}$

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{7}{5}))$

Multiply $\frac{7}{5}$ by $1$ .

$m_{perpendicular} = - \frac{7}{5}$

Step 5