Solution:
The equation of a line in point-slope form is given by;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \\ \text{where m is the slope} \\ \text{and } \\ (x_1,y_1)\text{ is the point} \\ m=\frac{4}{3} \\ x_1=-9 \\ y_1=5 \end{gathered}[/tex]Substituting these values into the formula;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-5=\frac{4}{3}(x-(-9)) \\ y-5=\frac{4}{3}(x+9) \end{gathered}[/tex]
Therefore, the equation of the line in point-slope form is;
[tex]y-5=\frac{4}{3}(x+9)[/tex]