Find Any Equation Parallel to the Line 16x-2y=1

$16 x - 2 y = 1$

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 $16 x$ from both sides of the equation.

$- 2 y = 1 - 16 x$

Divide each term in $- 2 y = 1 - 16 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 1 - 16 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{1}{- 2} + \frac{- 16 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{1}{- 2} + \frac{- 16 x}{- 2}$

Divide $y$ by $1$ .

$y = \frac{1}{- 2} + \frac{- 16 x}{- 2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{1}{2} + \frac{- 16 x}{- 2}$

Cancel the common factor of $- 16$ and $- 2$ .

Factor $- 2$ out of $- 16 x$ .

$y = - \frac{1}{2} + \frac{- 2 (8 x)}{- 2}$

Cancel the common factors.

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

$y = - \frac{1}{2} + \frac{- 2 (8 x)}{- 2 (1)}$

Cancel the common factor.

$y = - \frac{1}{2} + \frac{- 2 (8 x)}{- 2 \cdot 1}$

Rewrite the expression.

$y = - \frac{1}{2} + \frac{8 x}{1}$

Divide $8 x$ by $1$ .

$y = - \frac{1}{2} + 8 x$

Reorder $- \frac{1}{2}$ and $8 x$ .

$y = 8 x - \frac{1}{2}$

Step 3

Using the slope-intercept form, the slope is $8$ .

$m = 8$

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 $8$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = 8 \cdot (x - (0))$

Step 6

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

$y + 0 = 8 \cdot (x + 0)$

Step 7

Solve for $y$ .

Add $y$ and $0$ .

$y = 8 \cdot (x + 0)$

Add $x$ and $0$ .

$y = 8 x$

Step 8

Find Any Equation Parallel to the Line 16x-2y=1

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