Find the Parallel Line 3x+2y=6 , (-2,4)

$3 x + 2 y = 6$ , $(- 2, 4)$

Rewrite in slope-intercept form.

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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 $3 x$ from both sides of the equation.

$2 y = 6 - 3 x$

Divide each term by $2$ and simplify.

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Divide each term in $2 y = 6 - 3 x$ by $2$ .

$\frac{2 y}{2} = \frac{6}{2} + \frac{- 3 x}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 y}{2} = \frac{6}{2} + \frac{- 3 x}{2}$

Divide $y$ by $1$ .

$y = \frac{6}{2} + \frac{- 3 x}{2}$

Simplify $\frac{6}{2} + \frac{- 3 x}{2}$ .

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Simplify each term.

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Divide $6$ by $2$ .

$y = 3 + \frac{- 3 x}{2}$

Move the negative in front of the fraction.

$y = 3 - \frac{3 x}{2}$

Reorder $3$ and $- \frac{3 x}{2}$ .

$y = - \frac{3 x}{2} + 3$

Rewrite in slope-intercept form.

$y = - \frac{3}{2} x + 3$

Using the slope-intercept form, the slope is $- \frac{3}{2}$ .

$m = - \frac{3}{2}$

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

Use the slope $- \frac{3}{2}$ and a given point $(- 2, 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (4) = (- \frac{3}{2}) (x - (- 2))$

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

$y - 4 = - \frac{3}{2} \cdot (x + 2)$

Solve for $y$ .

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Simplify $- \frac{3}{2} \cdot (x + 2)$ .

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Simplify terms.

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Apply the distributive property.

$y - 4 = - \frac{3}{2} x - \frac{3}{2} \cdot 2$

Combine $x$ and $\frac{3}{2}$ .

$y - 4 = - \frac{x \cdot 3}{2} - \frac{3}{2} \cdot 2$

Cancel the common factor of $2$ .

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Move the leading negative in $- \frac{3}{2}$ into the numerator.

$y - 4 = - \frac{x \cdot 3}{2} + \frac{- 3}{2} \cdot 2$

Cancel the common factor.

$y - 4 = - \frac{x \cdot 3}{2} + \frac{- 3}{2} \cdot 2$

Rewrite the expression.

$y - 4 = - \frac{x \cdot 3}{2} - 3$

Move $3$ to the left of $x$ .

$y - 4 = - \frac{3 x}{2} - 3$

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

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Add $4$ to both sides of the equation.

$y = - \frac{3 x}{2} - 3 + 4$

Add $- 3$ and $4$ .

$y = - \frac{3 x}{2} + 1$

Reorder terms.

$y = - (\frac{3}{2} x) + 1$

Remove parentheses.

$y = - \frac{3}{2} x + 1$

Find the Parallel Line 3x+2y=6 , (-2,4)

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