# Question #a22d8

Jan 30, 2017

$C : y - 4 = \frac{1}{6} \left(x + 5\right)$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

$\text{here "m=1/6" and } \left({x}_{1} , {y}_{1}\right) = \left(- 5 , 4\right)$

Substitute these values into the equation.

$y - 4 = \frac{1}{6} \left(x - \left(- 5\right)\right)$

$\Rightarrow y - 4 = \frac{1}{6} \left(x + 5\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

We can distribute the bracket and simplify to obtain another version of the equation.

$y - 4 = \frac{1}{6} x + \frac{5}{6}$

$y = \frac{1}{6} x + \frac{5}{6} + 4$

$\Rightarrow y = \frac{1}{6} x + \frac{29}{6} \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$