# How do you write an equation in point slope form given (3/2, -1/3), (-2/3, 4)?

Jun 12, 2017

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

#### Explanation:

We are given the points $\left(\textcolor{\lim e g r e e n}{\frac{3}{2}} , \textcolor{red}{- \frac{1}{3}}\right)$ and $\left(\textcolor{b l u e}{- \frac{2}{3}} , \textcolor{\mathmr{and} a n \ge}{4}\right)$

Point-slope form looks like this:

$y - \textcolor{red}{{y}_{0}} = \left(\frac{\textcolor{\mathmr{and} a n \ge}{{y}_{1}} - \textcolor{red}{{y}_{0}}}{\textcolor{b l u e}{{x}_{1}} - \textcolor{\lim e g r e e n}{{x}_{0}}}\right) \left(x - \textcolor{\lim e g r e e n}{{x}_{0}}\right)$

So to write the equation of this line in point-slope form, we need to plug in the points given as follows:

$y - \left(\textcolor{red}{- \frac{1}{3}}\right) = \left(\frac{\textcolor{\mathmr{and} a n \ge}{4} - \left(\textcolor{red}{- \frac{1}{3}}\right)}{\textcolor{b l u e}{- \frac{2}{3}} - \textcolor{\lim e g r e e n}{\frac{3}{2}}}\right) \left(x - \textcolor{\lim e g r e e n}{\frac{3}{2}}\right)$

And simplify like this:

$y + \frac{1}{3} = \left(\frac{4 + \frac{1}{3}}{- \frac{4}{6} - \frac{9}{6}}\right) \left(x - \frac{3}{2}\right)$

$y + \frac{1}{3} = \left(\frac{\frac{13}{3}}{- \frac{13}{6}}\right) \left(x - \frac{3}{2}\right)$

$y + \frac{1}{3} = \left(\frac{6 \cdot \cancel{13}}{- 3 \cdot \cancel{13}}\right) \left(x - \frac{3}{2}\right)$

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