Answer
$\text{slope-intercept form: }
y=-\dfrac{5}{6}x+\dfrac{31}{6}
\\\\
\text{standard form: }
5x+6y=31$
Work Step by Step
Using $y-y_1=m(x-x_1)$ or the point-slope form of linear equations, the equation of the line passing through $(
-1,6
)$ and with a slope of $m=
-\dfrac{5}{6}
$ is
\begin{array}{l}\require{cancel}
y-6=-\dfrac{5}{6}(x-(-1))
\\\\
y-6=-\dfrac{5}{6}(x+1)
.\end{array}
In the form $y=mx+b$, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y-6=-\dfrac{5}{6}(x+1)
\\\\
y-6=-\dfrac{5}{6}x-\dfrac{5}{6}
\\\\
y=-\dfrac{5}{6}x-\dfrac{5}{6}+6
\\\\
y=-\dfrac{5}{6}x-\dfrac{5}{6}+\dfrac{36}{6}
\\\\
y=-\dfrac{5}{6}x+\dfrac{31}{6}
.\end{array}
In the form $Ax+By=C$, the equation above is equivalent to
\begin{array}{l}\require{cancel}
y=-\dfrac{5}{6}x+\dfrac{31}{6}
\\\\
6(y)=6\left( -\dfrac{5}{6}x+\dfrac{31}{6} \right)
\\\\
6y=-5x+31
\\\\
5x+6y=31
.\end{array}
Hence, the different forms of the equation of the line with the given conditions are
\begin{array}{l}\require{cancel}
\text{slope-intercept form: }
y=-\dfrac{5}{6}x+\dfrac{31}{6}
\\\\
\text{standard form: }
5x+6y=31
.\end{array}
