# What is the equation of the line passing through (2,-8) and (5,-3)?

Nov 30, 2015

The equation in slope intercept form is $y = \frac{5}{3} x - \frac{34}{3}$.

#### Explanation:

First find the slope, $m$.

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

$\left({x}_{1} , {y}_{1}\right) = \left(2 , - 8\right)$

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

$m = \frac{- 3 - \left(- 8\right)}{5 - 2}$

$m = \frac{- 3 + 8}{3}$

$m = \frac{5}{3}$

Us the point slope form of a linear equation, $y - {y}_{1} = m \left(x - {x}_{1}\right)$, where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ is one of the points on the line, such as $\left(2 , - 8\right)$.

$y - {y}_{1} = \frac{5}{3} \left(x - {x}_{1}\right)$

$y - \left(- 8\right) = \frac{5}{3} \left(x - 2\right)$

$y + 8 = \frac{5}{3} \left(x - 2\right)$

Multiply both sides times $3$.

$3 \left(y + 8\right) = 5 \left(x - 2\right)$

$3 y + 24 = 5 x - 10$

Subtract $24$ from both sides.

$3 y = 5 x - 10 - 24$

$3 y = 5 x - 34$

Divide both sides by $3$.

$y = \frac{5}{3} x - \frac{34}{3}$