# What is the equation of the line with slope  m= -7/17  that passes through  (-2,1) ?

Mar 4, 2016

The equation of the line is $y = - \frac{7}{17} x + \frac{3}{17}$

#### Explanation:

Let's start by writing the equation of a line:

$y = m x + b$

We know $m = - \frac{7}{17}$ and that the point $\left(- 2 , 1\right)$ will satisfy this equation. Let's substitute all of that into the equation and see if we can solve for $b$

$1 = - \frac{7}{17} \cdot \left(- 2\right) + b$

simplify the multiplication

$1 = \frac{14}{17} + b$

Then subtract $14 / 17$ from both sides

$b = 1 - \frac{14}{17} = \frac{17 - 14}{17} = \frac{3}{17}$

So the equation of the line we are looking for is

$y = - \frac{7}{17} x + \frac{3}{17}$