# What is the equation of the line with slope  m= -3/7  that passes through  (17/13,14/7) ?

Jun 20, 2018

$y = - \frac{3}{7} x + \setminus \frac{233}{91}$

#### Explanation:

When you know a given point $\left({x}_{0} , {y}_{0}\right)$ and the slope $m$, the equation of a line is

$y - {y}_{0} = m \left(x - {x}_{0}\right)$

In your case, $\left({x}_{0} , {y}_{0}\right) = \left(\setminus \frac{17}{13} , \setminus \frac{14}{7}\right) = \left(\setminus \frac{17}{13} , 2\right)$ and $m = - \frac{3}{7}$.

Let's plug these values in the formula:

$y - 2 = - \frac{3}{7} \left(x - \setminus \frac{17}{13}\right)$

Although this already is the equation of the line, you may want to write in the slope-intercept form, for example. Expanding the right hand side, we have

$y - 2 = - \frac{3}{7} x + \setminus \frac{51}{91}$

add $2$ to both sides to get

$y = - \frac{3}{7} x + \setminus \frac{233}{91}$