Find the Slope of a Perpendicular Line x-2y-7=0

$x - 2 y - 7 = 0$

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.

$y = m x + b$

Move all terms not containing $y$ to the right side of the equation.

Subtract $x$ from both sides of the equation.

$- 2 y - 7 = - x$

Add $7$ to both sides of the equation.

$- 2 y = - x + 7$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

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

Move the negative in front of the fraction.

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

Reorder terms.

$y = \frac{1}{2} x - \frac{7}{2}$

Step 2

Using the slope-intercept form, the slope is $\frac{1}{2}$ .

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

Step 3

The equation of a perpendicular line to $y = \frac{1}{2} x - \frac{7}{2}$ must have a slope that is the negative reciprocal of the original slope.

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

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

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

Multiply $- (1 \cdot 2)$ .

Multiply $2$ by $1$ .

$m_{perpendicular} = - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$m_{perpendicular} = - 2$

Step 5