# What is the equation of the line with slope  m= -5/17  that passes through  (3,1) ?

May 14, 2018

$y = - \frac{5}{17} x + \frac{32}{17}$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{here } m = - \frac{5}{17}$

$\Rightarrow y = - \frac{5}{17} + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(3,1)" into the partial equation}$

$1 = - \frac{15}{17} + b \Rightarrow b = \frac{17}{17} + \frac{15}{17} = \frac{32}{17}$

$\Rightarrow y = - \frac{5}{17} x + \frac{32}{17} \leftarrow \textcolor{red}{\text{ is equation of line}}$