# What is the equation of the line with slope  m= -1/8  that passes through  (7,-3) ?

Aug 4, 2016

$x + 8 y = - 17$

#### Explanation:

$y = m x + c$
or
$- 3 = - \frac{7}{8} + c$
or
$c = - 3 + \frac{7}{8}$
or
$c = - \frac{24 + 7}{8}$
or
$c = - \frac{17}{8}$
So the equation is
$y = - \frac{x}{8} - \frac{17}{8}$
or
$8 y = - x - 17$
or
$x + 8 y = - 17$

Aug 4, 2016

$y = - \frac{1}{8} x - \frac{17}{8}$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{point-slope form}}$ is

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

here $m = - \frac{1}{8} \text{ and } \left({x}_{1} , {y}_{1}\right) = \left(7 , - 3\right)$

substitute these values into the equation.

$y - \left(- 3\right) = - \frac{1}{8} \left(x - 7\right)$

$\Rightarrow y + 3 = - \frac{1}{8} x + \frac{7}{8} \Rightarrow y = - \frac{1}{8} x + \frac{7}{8} - 3$

$\Rightarrow y = - \frac{1}{8} x - \frac{17}{8} \text{ is the equation of the line}$