Find the Slope of a Perpendicular Line 2x-5y=7

$2 x - 5 y = 7$

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.

$y = m x + b$

Subtract $2 x$ from both sides of the equation.

$- 5 y = 7 - 2 x$

Divide each term in $- 5 y = 7 - 2 x$ by $- 5$ and simplify.

Divide each term in $- 5 y = 7 - 2 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{7}{- 5} + \frac{- 2 x}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{7}{- 5} + \frac{- 2 x}{- 5}$

Divide $y$ by $1$ .

$y = \frac{7}{- 5} + \frac{- 2 x}{- 5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{7}{5} + \frac{- 2 x}{- 5}$

Dividing two negative values results in a positive value.

$y = - \frac{7}{5} + \frac{2 x}{5}$

Write in $y = m x + b$ form.

Reorder $- \frac{7}{5}$ and $\frac{2 x}{5}$ .

$y = \frac{2 x}{5} - \frac{7}{5}$

Reorder terms.

$y = \frac{2}{5} x - \frac{7}{5}$

Using the slope-intercept form, the slope is $\frac{2}{5}$ .

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

The equation of a perpendicular line to $y = \frac{2}{5} x - \frac{7}{5}$ must have a slope that is the negative reciprocal of the original slope.

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

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

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

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

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