Answer :
We have to find the equation of the lines that pass through points (-5,3) and has a slope m=-6/5.
The easiest way to find the equation when we know one point and the slope is to write it in point-slope form:
[tex]y-y_0=m(x-x_0)[/tex]where (x0,y0) is the known point and m is the slope.
For our case, we can write:
[tex]\begin{gathered} y-3=-\frac{6}{5}\cdot(x-(-5)) \\ y=-\frac{6}{5}(x+5)+3 \\ y=-\frac{6}{5}x-6+3 \\ y=-\frac{6}{5}x-3 \end{gathered}[/tex]Answer: the equation of the line is y = (-6/5)*x-3