# How do you write the equation in point slope form given ( 1/2 , -1 ) , ( -2/3 , 6 )?

Jun 30, 2017

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

#### Explanation:

First, you need to know what the point-slope form of a line is. That is usually expressed as

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

This form of the equation of a line is the final goal. We need to find both the slope, $m$, and the point the line passes through at $\left({x}_{1} , {y}_{1}\right)$.

To find the slope, $m$, you need to have the slope formula.

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

Plugging in the points you were given, we get

$m = \frac{6 - \left(- 1\right)}{\left(- \frac{2}{3}\right) - \frac{1}{2}}$

$m = \frac{6 + 1}{- \frac{4}{6} - \frac{3}{6}}$

$m = \frac{7}{- \frac{7}{6}}$

$m = 7 \times \left(- \frac{6}{7}\right) = - 6$

The first point you were given was $\left(\frac{1}{2} , - 1\right)$, so you can plug this in for $\left({x}_{1} , {y}_{1}\right)$ in the point-slope equation above.

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

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

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