Answer
$y=-\dfrac{2}{7}x-\dfrac{23}{7}$
Work Step by Step
Using $y-y_1=m(x-x_1)$ or the Point-Slope form where $m$ is the slope and $(x_1,y_1)$ is a point on the line, then the equation of the line with the given slope equal to $
-\dfrac{2}{7}
$ and with the given point $\left(
6,-5
\right)$ is
\begin{array}{l}
y-(-5)=-\dfrac{2}{7}(x-6)
\\\\
y+5=-\dfrac{2}{7}x+\dfrac{12}{7}
\\\\
y=-\dfrac{2}{7}x+\dfrac{12}{7}-5
\\\\
y=-\dfrac{2}{7}x+\dfrac{12}{7}-\dfrac{35}{7}
\\\\
y=-\dfrac{2}{7}x-\dfrac{23}{7}
.\end{array}
