This a point-slope equation of a line problem.
The point-slope form of an equation of a line is given by the equation:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where:} \\ (x_1,y_1)\text{ is one point on the line} \\ m\text{ is the slope} \end{gathered}[/tex]
From the provided information, we have:
[tex]\begin{gathered} m=\frac{1}{3} \\ one\text{ point (-3,7)} \\ x_1=-3;y_1=7 \end{gathered}[/tex]
Thus, the equation of the line is:
[tex]\begin{gathered} y-7=\frac{1}{3}(x-(-3)) \\ y-7=\frac{1}{3}(x+3) \\ \text{cross}-\text{multiply} \\ 3(y-7)=x+3 \\ 3y-21=x+3 \\ 3y=x+3+21 \\ 3y=x+24 \\ y=\frac{x+24}{3} \\ y=\frac{x}{3}+\frac{24}{3} \\ y=\frac{x}{3}+8 \end{gathered}[/tex]
Hence, the equation of the line is:
[tex]y=\frac{x}{3}+8[/tex]
