Given the slope [tex]m[/tex] of a line and a point [tex](x_0,y_0)[/tex] belonging to the line, the equation of the line is
[tex]y-y_0=m(x-x_0)[/tex]
In your case, [tex]m=-\frac{5}{2}[/tex] and [tex](x_0,y_0)=(-6,6)[/tex]
So, the equation is
[tex]y-6=-\dfrac{5}{2}(x+6)\iff y=-\dfrac{5}{2}x-15+6 = -\dfrac{5}{2}x-9[/tex]
