# What is the slope intercept form of the line passing through (6,-1)  with a slope of -5/6 ?

May 24, 2017

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

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and b, the y-intercept.

$\text{here } m = - \frac{5}{6}$

$\Rightarrow y = - \frac{5}{6} x + b \leftarrow \text{ partial equation}$

$\text{to find b, substitute " (6,-1)" into the partial equation}$

$- 1 = \left(- \frac{5}{6} \times 6\right) + b$

$\Rightarrow b = - 1 + 5 = 4$

$\Rightarrow y = - \frac{5}{6} x + 4 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$