# What is the equation of the line that has slope 2/3 and passes through the point (-2,1)?

Dec 26, 2016

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

or

$y = \frac{2}{3} x + \frac{7}{3}$

#### Explanation:

To find this equation we can use the point-slope formula:

The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$
Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the information we are given in the problem produces:

$\left(y - \textcolor{red}{1}\right) = \textcolor{b l u e}{\frac{2}{3}} \left(x - \textcolor{red}{- 2}\right)$

$\left(y - \textcolor{red}{1}\right) = \textcolor{b l u e}{\frac{2}{3}} \left(x + \textcolor{red}{2}\right)$

To put this into slope-intercept form ($y = m x + b$) we can solve for $y$ as follows:

$\left(y - \textcolor{red}{1}\right) = \textcolor{b l u e}{\frac{2}{3}} x + \left(\textcolor{b l u e}{\frac{2}{3}} \times \textcolor{red}{2}\right)$

$y - \textcolor{red}{1} = \textcolor{b l u e}{\frac{2}{3}} x + \frac{4}{3}$

$y - \textcolor{red}{1} + \textcolor{g r e e n}{1} = \textcolor{b l u e}{\frac{2}{3}} x + \frac{4}{3} + \textcolor{g r e e n}{1}$

$y - 0 = \textcolor{b l u e}{\frac{2}{3}} x + \frac{4}{3} + \left(\textcolor{g r e e n}{1} \times \frac{3}{3}\right)$

$y = \textcolor{b l u e}{\frac{2}{3}} x + \frac{4}{3} + \textcolor{g r e e n}{\frac{3}{3}}$

$y = \textcolor{b l u e}{\frac{2}{3}} x + \frac{7}{3}$