Find the Slope of a Parallel Line 11x-12y=1

$11 x - 12 y = 1$

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 $11 x$ from both sides of the equation.

$- 12 y = 1 - 11 x$

Divide each term in $- 12 y = 1 - 11 x$ by $- 12$ and simplify.

Divide each term in $- 12 y = 1 - 11 x$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{1}{- 12} + \frac{- 11 x}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{1}{- 12} + \frac{- 11 x}{- 12}$

Divide $y$ by $1$ .

$y = \frac{1}{- 12} + \frac{- 11 x}{- 12}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{1}{12} + \frac{- 11 x}{- 12}$

Dividing two negative values results in a positive value.

$y = - \frac{1}{12} + \frac{11 x}{12}$

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

Reorder $- \frac{1}{12}$ and $\frac{11 x}{12}$ .

$y = \frac{11 x}{12} - \frac{1}{12}$

Reorder terms.

$y = \frac{11}{12} x - \frac{1}{12}$

Step 2

Using the slope-intercept form, the slope is $\frac{11}{12}$ .

$m = \frac{11}{12}$

Step 3

All lines that are parallel to $y = \frac{11}{12} x - \frac{1}{12}$ have the same slope of $\frac{11}{12}$ .

$m_{parallel} = \frac{11}{12}$

Step 4