Find the Parallel Line (4,-2) 4x+7y=9

$(4, - 2)$ $4 x + 7 y = 9$

Step 1

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 $4 x$ from both sides of the equation.

$7 y = 9 - 4 x$

Divide each term in $7 y = 9 - 4 x$ by $7$ and simplify.

Divide each term in $7 y = 9 - 4 x$ by $7$ .

$\frac{7 y}{7} = \frac{9}{7} + \frac{- 4 x}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{9}{7} + \frac{- 4 x}{7}$

Divide $y$ by $1$ .

$y = \frac{9}{7} + \frac{- 4 x}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{9}{7} - \frac{4 x}{7}$

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

Reorder $\frac{9}{7}$ and $- \frac{4 x}{7}$ .

$y = - \frac{4 x}{7} + \frac{9}{7}$

Reorder terms.

$y = - (\frac{4}{7} x) + \frac{9}{7}$

Remove parentheses.

$y = - \frac{4}{7} x + \frac{9}{7}$

Step 2

Using the slope-intercept form, the slope is $- \frac{4}{7}$ .

$m = - \frac{4}{7}$

Step 3

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

Step 4

Use the slope $- \frac{4}{7}$ and a given point $(4, - 2)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 2) = - \frac{4}{7} \cdot (x - (4))$

Step 5

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

$y + 2 = - \frac{4}{7} \cdot (x - 4)$

Step 6

Solve for $y$ .

Simplify $- \frac{4}{7} \cdot (x - 4)$ .

Rewrite.

$y + 2 = 0 + 0 - \frac{4}{7} \cdot (x - 4)$

Simplify by adding zeros.

$y + 2 = - \frac{4}{7} \cdot (x - 4)$

Apply the distributive property.

$y + 2 = - \frac{4}{7} x - \frac{4}{7} \cdot - 4$

Combine $x$ and $\frac{4}{7}$ .

$y + 2 = - \frac{x \cdot 4}{7} - \frac{4}{7} \cdot - 4$

Multiply $- \frac{4}{7} \cdot - 4$ .

Multiply $- 4$ by $- 1$ .

$y + 2 = - \frac{x \cdot 4}{7} + 4 (\frac{4}{7})$

Combine $4$ and $\frac{4}{7}$ .

$y + 2 = - \frac{x \cdot 4}{7} + \frac{4 \cdot 4}{7}$

Multiply $4$ by $4$ .

$y + 2 = - \frac{x \cdot 4}{7} + \frac{16}{7}$

Move $4$ to the left of $x$ .

$y + 2 = - \frac{4 x}{7} + \frac{16}{7}$

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

Subtract $2$ from both sides of the equation.

$y = - \frac{4 x}{7} + \frac{16}{7} - 2$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = - \frac{4 x}{7} + \frac{16}{7} - 2 \cdot \frac{7}{7}$

Combine $- 2$ and $\frac{7}{7}$ .

$y = - \frac{4 x}{7} + \frac{16}{7} + \frac{- 2 \cdot 7}{7}$

Combine the numerators over the common denominator.

$y = - \frac{4 x}{7} + \frac{16 - 2 \cdot 7}{7}$

Simplify the numerator.

Multiply $- 2$ by $7$ .

$y = - \frac{4 x}{7} + \frac{16 - 14}{7}$

Subtract $14$ from $16$ .

$y = - \frac{4 x}{7} + \frac{2}{7}$

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

Reorder terms.

$y = - (\frac{4}{7} x) + \frac{2}{7}$

Remove parentheses.

$y = - \frac{4}{7} x + \frac{2}{7}$

Step 7

Find the Parallel Line (4,-2) 4x+7y=9

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