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{5}{7} \\ (x_1,y_1)=(-2,5) \end{gathered}[/tex][tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-5=\frac{5}{7}(x-(-2)) \\ y-5=\frac{5}{7}(x+2) \\ y-5=\frac{5}{7}x+\frac{10}{7} \\ \text{ Add 5 to both sides of the equation} \\ y-5+5=\frac{5}{7}x+\frac{10}{7}+5 \\ y=\frac{5}{7}x+\frac{45}{7} \end{gathered}[/tex]
Therefore, the equation of the line in its point-slope form for this exercise is
[tex]y=\frac{5}{7}x+\frac{45}{7}[/tex]
