# How do you find a standard form equation for the line with (-2,2) and is parallel to the line whose equation is 2x-3y-7=0?

Sep 20, 2016

$2 x - 3 y + 10 = 0$

#### Explanation:

$2 x - 3 y - 7 = 0$ and any line parallel to it has a slope of $\textcolor{g r e e n}{m = \frac{2}{3}}$
$\textcolor{w h i t e}{\text{XXX}}$We know this either because:
$\textcolor{w h i t e}{\text{XXX")color(white)("XX}}$we know $A x + B y + c = 0$ has a slope of $\textcolor{g r e e n}{- \frac{A}{B}}$
$\textcolor{w h i t e}{\text{XXX}}$or
$\textcolor{w h i t e}{\text{XXX")color(white)("XX}}$ by converting into slope-intercept form: $y = \textcolor{g r e e n}{m} x + b$
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If a line has a slope of $\textcolor{g r e e n}{\frac{2}{3}}$ and passes through $\left(\textcolor{red}{- 2} , \textcolor{b l u e}{2}\right)$
then it has a slope-point form of
color(white)("XXX")y-color(blue)(2)=color(green)(2/3)(x-color(red)(""(-2)))

Simplifying
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{\frac{2}{3}} \left(x + 2\right) + 2$

$\textcolor{w h i t e}{\text{XXX}} 3 y = \left(2 x + 4\right) + 6$

or (in standard form)
$\textcolor{w h i t e}{\text{XXX}} 2 x - 3 y + 10 = 0$

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For verification/support, here are the graphs: 