# How do you write the equation of a point slope form passing through (-2,8) and parallel to the line 5x-6y-7=0?

Dec 30, 2016

$y = \frac{5}{6} x + \frac{29}{3}$

#### Explanation:

Parallel lines have the same slope.

Get the slope of the given line

$5 x - 6 y - 7 = 0$

$\implies 6 y = 5 x - 7$

$\implies y = \frac{5}{6} x - \frac{7}{6}$

$\implies m = \frac{5}{6}$

$y = \frac{5}{6} x + b$

Get the y-intercept using the given point

$\implies 8 = \frac{5}{6} \left(- 2\right) + b$

$\implies 8 = - \frac{5}{3} + b$

$\implies 24 = - 5 + 3 b$

$\implies 29 = 3 b$

$\implies b = \frac{29}{3}$

$y = \frac{5}{6} x + \frac{29}{3}$