Find Any Equation Parallel to the Line 3x-y=-6

$3 x - y = - 6$

Choose a point that the parallel line will pass through.

$(0, 0)$

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 $3 x$ from both sides of the equation.

$- y = - 6 - 3 x$

Divide each term in $- y = - 6 - 3 x$ by $- 1$ and simplify.

Divide each term in $- y = - 6 - 3 x$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $- 6$ by $- 1$ .

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

Move the negative one from the denominator of $\frac{- 3 x}{- 1}$ .

$y = 6 - 1 \cdot (- 3 x)$

Rewrite $- 1 \cdot (- 3 x)$ as $- (- 3 x)$ .

$y = 6 - (- 3 x)$

Multiply $- 3$ by $- 1$ .

$y = 6 + 3 x$

Reorder $6$ and $3 x$ .

$y = 3 x + 6$

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

$m = 3$

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

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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

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

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

Solve for $y$ .

Add $y$ and $0$ .

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

Add $x$ and $0$ .

$y = 3 x$

Find Any Equation Parallel to the Line 3x-y=-6

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