Find the Parallel Line 4x-y=-8 (0,0)

$4 x - y = - 8$ $(0, 0)$

Rewrite in slope-intercept form.

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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 $4 x$ from both sides of the equation.

$- y = - 8 - 4 x$

Multiply each term in $- y = - 8 - 4 x$ by $- 1$

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Multiply each term in $- y = - 8 - 4 x$ by $- 1$ .

$(- y) \cdot - 1 = (- 8) \cdot - 1 + (- 4 x) \cdot - 1$

Multiply $(- y) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 y = (- 8) \cdot - 1 + (- 4 x) \cdot - 1$

Multiply $y$ by $1$ .

$y = (- 8) \cdot - 1 + (- 4 x) \cdot - 1$

Simplify $(- 8) \cdot - 1 + (- 4 x) \cdot - 1$ .

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Simplify each term.

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Multiply $- 8$ by $- 1$ .

$y = 8 + (- 4 x) \cdot - 1$

Multiply $- 1$ by $- 4$ .

$y = 8 + 4 x$

Reorder $8$ and $4 x$ .

$y = 4 x + 8$

Using the slope-intercept form, the slope is $4$ .

$m = 4$

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

Use the slope $4$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = (4) (x - (0))$

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

$y + 0 = 4 \cdot (x + 0)$

Solve for $y$ .

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Add $y$ and $0$ .

$y = 4 \cdot (x + 0)$

Add $x$ and $0$ .

$y = 4 x$

Find the Parallel Line 4x-y=-8 (0,0)

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