Find Any Equation Parallel to the Line 9x+3y=-22

$9 x + 3 y = - 22$

Step 1

Choose a point that the parallel line will pass through.

$(0, 0)$

Step 2

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 $9 x$ from both sides of the equation.

$3 y = - 22 - 9 x$

Divide each term in $3 y = - 22 - 9 x$ by $3$ and simplify.

Divide each term in $3 y = - 22 - 9 x$ by $3$ .

$\frac{3 y}{3} = \frac{- 22}{3} + \frac{- 9 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 22}{3} + \frac{- 9 x}{3}$

Divide $y$ by $1$ .

$y = \frac{- 22}{3} + \frac{- 9 x}{3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{22}{3} + \frac{- 9 x}{3}$

Cancel the common factor of $- 9$ and $3$ .

Factor $3$ out of $- 9 x$ .

$y = - \frac{22}{3} + \frac{3 (- 3 x)}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$y = - \frac{22}{3} + \frac{3 (- 3 x)}{3 (1)}$

Cancel the common factor.

$y = - \frac{22}{3} + \frac{3 (- 3 x)}{3 \cdot 1}$

Rewrite the expression.

$y = - \frac{22}{3} + \frac{- 3 x}{1}$

Divide $- 3 x$ by $1$ .

$y = - \frac{22}{3} - 3 x$

Reorder $- \frac{22}{3}$ and $- 3 x$ .

$y = - 3 x - \frac{22}{3}$

Step 3

Using the slope-intercept form, the slope is $- 3$ .

$m = - 3$

Step 4

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

Step 5

Use the slope $- 3$ and a given point $(0, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - 3 \cdot (x - (0))$

Step 6

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

$y + 0 = - 3 \cdot (x + 0)$

Step 7

Solve for $y$ .

Add $y$ and $0$ .

$y = - 3 \cdot (x + 0)$

Add $x$ and $0$ .

$y = - 3 x$

Step 8

Find Any Equation Parallel to the Line 9x+3y=-22

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