To solve the exercise you can use the point-slope formula, that is,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} m=\frac{4}{5} \\ (x_1,y_1)=(-5,2) \end{gathered}[/tex][tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-2_{}=\frac{4}{5}(x-(-5)) \\ y-2_{}=\frac{4}{5}(x+5) \\ y-2_{}=\frac{4}{5}x+4 \\ \text{ Add 2 from both sides of the equation} \\ y-2_{}+2=\frac{4}{5}x+4+2 \\ y=\frac{4}{5}x+6 \end{gathered}[/tex]Therefore, the equation of the line that passes through the point (-5, 2) and has a slope of 4/5 is
[tex]y=\frac{4}{5}x+6[/tex]
