The slope intercept form of a line is:
[tex]y=mx+b[/tex]Where
m is slope
b in y-intercept
We are already given slope, so we can write:
[tex]y=-\frac{5}{7}x+b[/tex]Now, to figure out b, we replace x with -2 and y with 5 (point given),
[tex]\begin{gathered} y=-\frac{5}{7}x+b \\ 5=-\frac{5}{7}(-2)+b \\ 5=\frac{10}{7}+b \\ b=5-\frac{10}{7} \\ b=\frac{35-10}{7} \\ b=\frac{25}{7} \end{gathered}[/tex]So,
FInal Equation:
[tex]y=-\frac{5}{7}x+\frac{25}{7}[/tex]