Find the Slope of a Perpendicular Line 8x+2y=7

$8 x + 2 y = 7$

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.

$y = m x + b$

Subtract $8 x$ from both sides of the equation.

$2 y = 7 - 8 x$

Divide each term in $2 y = 7 - 8 x$ by $2$ and simplify.

Divide each term in $2 y = 7 - 8 x$ by $2$ .

$\frac{2 y}{2} = \frac{7}{2} + \frac{- 8 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{7}{2} + \frac{- 8 x}{2}$

Divide $y$ by $1$ .

$y = \frac{7}{2} + \frac{- 8 x}{2}$

Simplify the right side.

Cancel the common factor of $- 8$ and $2$ .

Factor $2$ out of $- 8 x$ .

$y = \frac{7}{2} + \frac{2 (- 4 x)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y = \frac{7}{2} + \frac{2 (- 4 x)}{2 (1)}$

Cancel the common factor.

$y = \frac{7}{2} + \frac{2 (- 4 x)}{2 \cdot 1}$

Rewrite the expression.

$y = \frac{7}{2} + \frac{- 4 x}{1}$

Divide $- 4 x$ by $1$ .

$y = \frac{7}{2} - 4 x$

Reorder $\frac{7}{2}$ and $- 4 x$ .

$y = - 4 x + \frac{7}{2}$

Step 2

Using the slope-intercept form, the slope is $- 4$ .

$m = - 4$

Step 3

The equation of a perpendicular line to $y = - 4 x + \frac{7}{2}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- 4}$

Step 4

Simplify the result.

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{4}$

Multiply $- - \frac{1}{4}$ .

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{1}{4})$

Multiply $\frac{1}{4}$ by $1$ .

$m_{perpendicular} = \frac{1}{4}$

Step 5

Find the Slope of a Perpendicular Line 8x+2y=7

Related Questions

Support LCMGCF.com by disabling your adblocker.