Find the Slope of a Perpendicular Line x-6y=3

$x - 6 y = 3$

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.

$y = m x + b$

Subtract $x$ from both sides of the equation.

$- 6 y = 3 - x$

Divide each term in $- 6 y = 3 - x$ by $- 6$ and simplify.

Divide each term in $- 6 y = 3 - x$ by $- 6$ .

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

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ and $- 6$ .

Factor $3$ out of $3$ .

$y = \frac{3 (1)}{- 6} + \frac{- x}{- 6}$

Cancel the common factors.

Factor $3$ out of $- 6$ .

$y = \frac{3 \cdot 1}{3 \cdot - 2} + \frac{- x}{- 6}$

Cancel the common factor.

$y = \frac{3 \cdot 1}{3 \cdot - 2} + \frac{- x}{- 6}$

Rewrite the expression.

$y = \frac{1}{- 2} + \frac{- x}{- 6}$

Move the negative in front of the fraction.

$y = - \frac{1}{2} + \frac{- x}{- 6}$

Dividing two negative values results in a positive value.

$y = - \frac{1}{2} + \frac{x}{6}$

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

Reorder $- \frac{1}{2}$ and $\frac{x}{6}$ .

$y = \frac{x}{6} - \frac{1}{2}$

Reorder terms.

$y = \frac{1}{6} x - \frac{1}{2}$

Step 2

Using the slope-intercept form, the slope is $\frac{1}{6}$ .

$m = \frac{1}{6}$

Step 3

The equation of a perpendicular line to $y = \frac{1}{6} x - \frac{1}{2}$ must have a slope that is the negative reciprocal of the original slope.

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

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

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

Multiply $- (1 \cdot 6)$ .

Multiply $6$ by $1$ .

$m_{perpendicular} = - 1 \cdot 6$

Multiply $- 1$ by $6$ .

$m_{perpendicular} = - 6$

Step 5

Find the Slope of a Perpendicular Line x-6y=3

Related Questions

Support LCMGCF.com by disabling your adblocker.