Find the Slope of a Perpendicular Line 7x-6y=-4

$7 x - 6 y = - 4$

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 $7 x$ from both sides of the equation.

$- 6 y = - 4 - 7 x$

Divide each term in $- 6 y = - 4 - 7 x$ by $- 6$ and simplify.

Divide each term in $- 6 y = - 4 - 7 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{- 4}{- 6} + \frac{- 7 x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{- 4}{- 6} + \frac{- 7 x}{- 6}$

Divide $y$ by $1$ .

$y = \frac{- 4}{- 6} + \frac{- 7 x}{- 6}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 4$ and $- 6$ .

Factor $- 2$ out of $- 4$ .

$y = \frac{- 2 (2)}{- 6} + \frac{- 7 x}{- 6}$

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

$y = \frac{- 2 \cdot 2}{- 2 \cdot 3} + \frac{- 7 x}{- 6}$

Cancel the common factor.

$y = \frac{- 2 \cdot 2}{- 2 \cdot 3} + \frac{- 7 x}{- 6}$

Rewrite the expression.

$y = \frac{2}{3} + \frac{- 7 x}{- 6}$

Dividing two negative values results in a positive value.

$y = \frac{2}{3} + \frac{7 x}{6}$

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

Reorder $\frac{2}{3}$ and $\frac{7 x}{6}$ .

$y = \frac{7 x}{6} + \frac{2}{3}$

Reorder terms.

$y = \frac{7}{6} x + \frac{2}{3}$

Step 2

Using the slope-intercept form, the slope is $\frac{7}{6}$ .

$m = \frac{7}{6}$

Step 3

The equation of a perpendicular line to $y = \frac{7}{6} x + \frac{2}{3}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{\frac{7}{6}}$

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{6}{7}))$

Multiply $\frac{6}{7}$ by $1$ .

$m_{perpendicular} = - \frac{6}{7}$

Step 5

Find the Slope of a Perpendicular Line 7x-6y=-4

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