Find Any Equation Parallel to the Line 8x-2y=30

$8 x - 2 y = 30$

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 $8 x$ from both sides of the equation.

$- 2 y = 30 - 8 x$

Divide each term in $- 2 y = 30 - 8 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 30 - 8 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{30}{- 2} + \frac{- 8 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{30}{- 2} + \frac{- 8 x}{- 2}$

Divide $y$ by $1$ .

$y = \frac{30}{- 2} + \frac{- 8 x}{- 2}$

Simplify the right side.

Simplify each term.

Divide $30$ by $- 2$ .

$y = - 15 + \frac{- 8 x}{- 2}$

Cancel the common factor of $- 8$ and $- 2$ .

Factor $- 2$ out of $- 8 x$ .

$y = - 15 + \frac{- 2 (4 x)}{- 2}$

Cancel the common factors.

Factor $- 2$ out of $- 2$ .

$y = - 15 + \frac{- 2 (4 x)}{- 2 (1)}$

Cancel the common factor.

$y = - 15 + \frac{- 2 (4 x)}{- 2 \cdot 1}$

Rewrite the expression.

$y = - 15 + \frac{4 x}{1}$

Divide $4 x$ by $1$ .

$y = - 15 + 4 x$

Reorder $- 15$ and $4 x$ .

$y = 4 x - 15$

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

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

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

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

Solve for $y$ .

Add $y$ and $0$ .

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

Add $x$ and $0$ .

$y = 4 x$

Find Any Equation Parallel to the Line 8x-2y=30

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