# What is the equation of the line passing through (5,4) and (-9,-2)?

Jun 9, 2016

The equation of the straight line is : $7 y - 3 x + 11 = 0$

#### Explanation:

Let $A \left(x 1 , y 1\right) = A \left(5 , 4\right)$
and $B \left(x 2 , y 2\right) = B \left(- 9 , - 2\right)$

First find the slope of the line, using the formula :

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

$m = \frac{- 6}{-} 14 = \frac{3}{7}$

Now using the point-slope form of a straight line :
$y - y 1 = m \left(x - x 1\right)$

$y - 4 = \frac{3}{7} \cdot \left(x - 5\right)$

On simplifying, we get,
$7 y - 3 x + 11 = 0$

graph{3/7*(x-5) +4 [-10, 10, -5, 5]}