# Question #ecc32

Dec 14, 2016

$y - 5 = \frac{2}{3} \left(x + 2\right)$ or $y = \frac{2}{3} x + \frac{19}{3}$

#### Explanation:

We can use the point-slope formula to solve this problem. The point-slope formula is:

$\textcolor{red}{y - {y}_{1} = m \left(x - {x}_{1}\right)}$

Where $m$ is the slope, which for this problem is 2/3 and $\left({x}_{1} , {y}_{1}\right)$ is a point on the line, which for this problem is (-2, 5).

Substituting gives:

$y - 5 = \frac{2}{3} \left(x - - 2\right)$

$y - 5 = \frac{2}{3} \left(x + 2\right)$

or, solving for $y$ to put the equation in slope-intercept for is:

$y - 5 = \frac{2}{3} x + 2 \cdot \frac{2}{3}$

$y - 5 = \frac{2}{3} x + \frac{4}{3}$

$y - 5 + 5 = \frac{2}{3} x + \frac{4}{3} + 5$

$y - 0 = \frac{2}{3} x + \frac{4}{3} + \left(\frac{3}{3} \cdot 5\right)$

$y = \frac{2}{3} x + \frac{4}{3} + \frac{15}{3}$

$y = \frac{2}{3} x + \frac{19}{3}$