# How do you write the equation in slope intercept form given (4, 5), (2, 2)?

Feb 27, 2016

$y = \frac{3}{2} x - 1$

#### Explanation:

$\left(4 , 5\right) \equiv \left({x}_{1} , {y}_{1}\right)$
$\left(2 , 2\right) \equiv \left({x}_{2} , {y}_{2}\right)$

By two point form,

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

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

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

$2 \left(y - 5\right) = 3 \left(x - 4\right)$

$2 y - 10 = 3 x - 12$

$2 y = 3 x - 12 + 10$

$2 y = 3 x - 2$

Divide by 2

$y = \frac{3}{2} x - 1$ is in slope-intercept form