The equation of a line that passes throught two points is given as:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Plugging the values of the points given we have:
[tex]\begin{gathered} y-7=\frac{4-7}{-6-3}(x-3) \\ y-7=\frac{-3}{-9}(x-3) \\ y-7=\frac{1}{3}(x-3) \\ y-7=\frac{1}{3}x-1 \\ y=\frac{1}{3}x-1+7 \\ y=\frac{1}{3}x+6 \end{gathered}[/tex]Therefore the equation of the line in slope intercept form is:
[tex]y=\frac{1}{3}x+6[/tex]