The equation, given slope and 1 point, of a line is given as:
[tex]y-y_1=m(x-x_1)_{}[/tex]Where
m is the slope (Given, 1/3 rd)
(x_1, y_1) is the point (Given, F(3,-6)
Now, let's substitute the given information into the equation:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-6)=\frac{1}{3}(x-3) \end{gathered}[/tex]Now, we simplify and put the answer in the form y = mx + b. Shown below:
[tex]\begin{gathered} y-(-6)=\frac{1}{3}(x-3) \\ y+6=\frac{1}{3}x-1 \\ y=\frac{1}{3}x-1-6 \\ y=\frac{1}{3}x-7 \end{gathered}[/tex]Answer:
[tex]y=\frac{1}{3}x-7[/tex]