Find the Parallel Line 4x-2y=9 , (2,1)

$4 x - 2 y = 9$ , $(2, 1)$

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.

$- 2 y = 9 - 4 x$

Divide each term in $- 2 y = 9 - 4 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 9 - 4 x$ by $- 2$ .

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Cancel the common factor of $- 4$ and $- 2$ .

Factor $- 2$ out of $- 4 x$ .

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

Cancel the common factors.

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

$y = - \frac{9}{2} + \frac{- 2 (2 x)}{- 2 (1)}$

Cancel the common factor.

$y = - \frac{9}{2} + \frac{- 2 (2 x)}{- 2 \cdot 1}$

Rewrite the expression.

$y = - \frac{9}{2} + \frac{2 x}{1}$

Divide $2 x$ by $1$ .

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

Reorder $- \frac{9}{2}$ and $2 x$ .

$y = 2 x - \frac{9}{2}$

Step 2

Using the slope-intercept form, the slope is $2$ .

$m = 2$

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

$y - (1) = 2 \cdot (x - (2))$

Step 5

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

$y - 1 = 2 \cdot (x - 2)$

Step 6

Solve for $y$ .

Simplify $2 \cdot (x - 2)$ .

Rewrite.

$y - 1 = 0 + 0 + 2 \cdot (x - 2)$

Simplify by adding zeros.

$y - 1 = 2 \cdot (x - 2)$

Apply the distributive property.

$y - 1 = 2 x + 2 \cdot - 2$

Multiply $2$ by $- 2$ .

$y - 1 = 2 x - 4$

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

Add $1$ to both sides of the equation.

$y = 2 x - 4 + 1$

Add $- 4$ and $1$ .

$y = 2 x - 3$

Step 7

Find the Parallel Line 4x-2y=9 , (2,1)

Related Questions

Support LCMGCF.com by disabling your adblocker.