Find the Parallel Line (-5,-7) 6x+5y=11

$(- 5, - 7)$ $6 x + 5 y = 11$

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 $6 x$ from both sides of the equation.

$5 y = 11 - 6 x$

Divide each term in $5 y = 11 - 6 x$ by $5$ and simplify.

Divide each term in $5 y = 11 - 6 x$ by $5$ .

$\frac{5 y}{5} = \frac{11}{5} + \frac{- 6 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{11}{5} + \frac{- 6 x}{5}$

Divide $y$ by $1$ .

$y = \frac{11}{5} + \frac{- 6 x}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{11}{5} - \frac{6 x}{5}$

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

Reorder $\frac{11}{5}$ and $- \frac{6 x}{5}$ .

$y = - \frac{6 x}{5} + \frac{11}{5}$

Reorder terms.

$y = - (\frac{6}{5} x) + \frac{11}{5}$

Remove parentheses.

$y = - \frac{6}{5} x + \frac{11}{5}$

Step 2

Using the slope-intercept form, the slope is $- \frac{6}{5}$ .

$m = - \frac{6}{5}$

Step 3

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Step 4

Use the slope $- \frac{6}{5}$ and a given point $(- 5, - 7)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 7) = - \frac{6}{5} \cdot (x - (- 5))$

Step 5

Simplify the equation and keep it in point-slope form.

$y + 7 = - \frac{6}{5} \cdot (x + 5)$

Step 6

Solve for $y$ .

Simplify $- \frac{6}{5} \cdot (x + 5)$ .

Rewrite.

$y + 7 = 0 + 0 - \frac{6}{5} \cdot (x + 5)$

Simplify terms.

Apply the distributive property.

$y + 7 = - \frac{6}{5} x - \frac{6}{5} \cdot 5$

Combine $x$ and $\frac{6}{5}$ .

$y + 7 = - \frac{x \cdot 6}{5} - \frac{6}{5} \cdot 5$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$y + 7 = - \frac{x \cdot 6}{5} + \frac{- 6}{5} \cdot 5$

Cancel the common factor.

$y + 7 = - \frac{x \cdot 6}{5} + \frac{- 6}{5} \cdot 5$

Rewrite the expression.

$y + 7 = - \frac{x \cdot 6}{5} - 6$

Move $6$ to the left of $x$ .

$y + 7 = - \frac{6 x}{5} - 6$

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

Subtract $7$ from both sides of the equation.

$y = - \frac{6 x}{5} - 6 - 7$

Subtract $7$ from $- 6$ .

$y = - \frac{6 x}{5} - 13$

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

Reorder terms.

$y = - (\frac{6}{5} x) - 13$

Remove parentheses.

$y = - \frac{6}{5} x - 13$

Step 7

Find the Parallel Line (-5,-7) 6x+5y=11

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