Find the Parallel Line 4x-9y=5 (-4,2)

$4 x - 9 y = 5$ $(- 4, 2)$

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.

$- 9 y = 5 - 4 x$

Divide each term in $- 9 y = 5 - 4 x$ by $- 9$ and simplify.

Divide each term in $- 9 y = 5 - 4 x$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{5}{- 9} + \frac{- 4 x}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{5}{- 9} + \frac{- 4 x}{- 9}$

Divide $y$ by $1$ .

$y = \frac{5}{- 9} + \frac{- 4 x}{- 9}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{5}{9} + \frac{- 4 x}{- 9}$

Dividing two negative values results in a positive value.

$y = - \frac{5}{9} + \frac{4 x}{9}$

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

Reorder $- \frac{5}{9}$ and $\frac{4 x}{9}$ .

$y = \frac{4 x}{9} - \frac{5}{9}$

Reorder terms.

$y = \frac{4}{9} x - \frac{5}{9}$

Step 2

Using the slope-intercept form, the slope is $\frac{4}{9}$ .

$m = \frac{4}{9}$

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 $\frac{4}{9}$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (2) = \frac{4}{9} \cdot (x - (- 4))$

Step 5

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

$y - 2 = \frac{4}{9} \cdot (x + 4)$

Step 6

Solve for $y$ .

Simplify $\frac{4}{9} \cdot (x + 4)$ .

Rewrite.

$y - 2 = 0 + 0 + \frac{4}{9} \cdot (x + 4)$

Simplify by adding zeros.

$y - 2 = \frac{4}{9} \cdot (x + 4)$

Apply the distributive property.

$y - 2 = \frac{4}{9} x + \frac{4}{9} \cdot 4$

Combine $\frac{4}{9}$ and $x$ .

$y - 2 = \frac{4 x}{9} + \frac{4}{9} \cdot 4$

Multiply $\frac{4}{9} \cdot 4$ .

Combine $\frac{4}{9}$ and $4$ .

$y - 2 = \frac{4 x}{9} + \frac{4 \cdot 4}{9}$

Multiply $4$ by $4$ .

$y - 2 = \frac{4 x}{9} + \frac{16}{9}$

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

Add $2$ to both sides of the equation.

$y = \frac{4 x}{9} + \frac{16}{9} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$y = \frac{4 x}{9} + \frac{16}{9} + 2 \cdot \frac{9}{9}$

Combine $2$ and $\frac{9}{9}$ .

$y = \frac{4 x}{9} + \frac{16}{9} + \frac{2 \cdot 9}{9}$

Combine the numerators over the common denominator.

$y = \frac{4 x}{9} + \frac{16 + 2 \cdot 9}{9}$

Simplify the numerator.

Multiply $2$ by $9$ .

$y = \frac{4 x}{9} + \frac{16 + 18}{9}$

Add $16$ and $18$ .

$y = \frac{4 x}{9} + \frac{34}{9}$

Reorder terms.

$y = \frac{4}{9} x + \frac{34}{9}$

Step 7

Find the Parallel Line 4x-9y=5 (-4,2)

Related Questions

Support LCMGCF.com by disabling your adblocker.