Find the Parallel Line -3x-y=-4 , P=(1,4)

$- 3 x - y = - 4$ , $P = (1, 4)$

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.

$y = m x + b$

Add $3 x$ to both sides of the equation.

$- y = - 4 + 3 x$

Divide each term in $- y = - 4 + 3 x$ by $- 1$ and simplify.

Divide each term in $- y = - 4 + 3 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 4}{- 1} + \frac{3 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 4}{- 1} + \frac{3 x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{- 4}{- 1} + \frac{3 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $- 4$ by $- 1$ .

$y = 4 + \frac{3 x}{- 1}$

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

$y = 4 - 1 \cdot (3 x)$

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

$y = 4 - (3 x)$

Multiply $3$ by $- 1$ .

$y = 4 - 3 x$

Reorder $4$ and $- 3 x$ .

$y = - 3 x + 4$

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 $P = (1, 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (4) = - 3 \cdot (x - (1))$

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

$y - 4 = - 3 \cdot (x - 1)$

Solve for $y$ .

Simplify $- 3 \cdot (x - 1)$ .

Rewrite.

$y - 4 = 0 + 0 - 3 \cdot (x - 1)$

Simplify by adding zeros.

$y - 4 = - 3 \cdot (x - 1)$

Apply the distributive property.

$y - 4 = - 3 x - 3 \cdot - 1$

Multiply $- 3$ by $- 1$ .

$y - 4 = - 3 x + 3$

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

Add $4$ to both sides of the equation.

$y = - 3 x + 3 + 4$

Add $3$ and $4$ .

$y = - 3 x + 7$

Find the Parallel Line -3x-y=-4 , P=(1,4)

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