# How do you write the equation in point slope form given (-1,2) and parallel to the line whose equation is 3x-2y=7?

Sep 4, 2017

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

#### Explanation:

$\text{the first thing to know is that}$

• " parallel lines have equal slopes"

$\text{to obtain the slope rearrange } 3 x - 2 y = 7$
$\text{into "color(blue)"slope-intercept form}$

•color(white)(x)y=mx+b

$\text{where m represents the slope and b the y-intercept}$

$3 x - 2 y = 7$

$\Rightarrow - 2 y = - 3 x + 7$

$\Rightarrow y = \frac{3}{2} x - \frac{7}{2} \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$

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

$\text{expressing the equation in "color(blue)"point-slope form}$

•color(white)(x)y=y_1=m(x-x_1)

$\text{with "m=3/2" and } \left({x}_{1} , {y}_{1}\right) = \left(- 1 , 2\right)$

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