# How do you write the equation in point-slope form of the line which passes through (-2, 3) and is parallel to 3x + 2y = 10?

Jun 12, 2017

The equation of line passing through $\left(- 2 , 3\right)$ is $y - 3 = - \frac{3}{2} \left(x + 2\right)$

#### Explanation:

The slope of the line $3 x + 2 y = 10 \mathmr{and} 2 y = - 3 x + 10 \mathmr{and} y = - \frac{3}{2} x + 5$ is $m = - \frac{3}{2} \left[y = m x + c\right]$.

Parallel lines have equal slopes.

The equation of line passing through ${x}_{1} , {y}_{1}$ is $y - {y}_{1} = m \left(x - {x}_{1}\right)$

So the equation of line passing through $\left(- 2 , 3\right)$ is $y - 3 = - \frac{3}{2} \left(x + 2\right)$[Ans]