Find Any Equation Parallel to the Line 5x-7y=2

$5 x - 7 y = 2$

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 $5 x$ from both sides of the equation.

$- 7 y = 2 - 5 x$

Divide each term in $- 7 y = 2 - 5 x$ by $- 7$ and simplify.

Divide each term in $- 7 y = 2 - 5 x$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{2}{- 7} + \frac{- 5 x}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{2}{- 7} + \frac{- 5 x}{- 7}$

Divide $y$ by $1$ .

$y = \frac{2}{- 7} + \frac{- 5 x}{- 7}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{2}{7} + \frac{- 5 x}{- 7}$

Dividing two negative values results in a positive value.

$y = - \frac{2}{7} + \frac{5 x}{7}$

Write in $y = m x + b$ form.

Reorder $- \frac{2}{7}$ and $\frac{5 x}{7}$ .

$y = \frac{5 x}{7} - \frac{2}{7}$

Reorder terms.

$y = \frac{5}{7} x - \frac{2}{7}$

Step 3

Using the slope-intercept form, the slope is $\frac{5}{7}$ .

$m = \frac{5}{7}$

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 $\frac{5}{7}$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = \frac{5}{7} \cdot (x - (0))$

Step 6

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

$y + 0 = \frac{5}{7} \cdot (x + 0)$

Step 7

Solve for $y$ .

Add $y$ and $0$ .

$y = \frac{5}{7} \cdot (x + 0)$

Simplify $\frac{5}{7} \cdot (x + 0)$ .

Add $x$ and $0$ .

$y = \frac{5}{7} \cdot x$

Combine $\frac{5}{7}$ and $x$ .

$y = \frac{5 x}{7}$

Reorder terms.

$y = \frac{5}{7} x$

Step 8

Find Any Equation Parallel to the Line 5x-7y=2

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