Let us first solve for the slope (m) of the perpendicular line.
[tex]\text{ 5x + 3y = -21}[/tex][tex]\text{ 3y = -5x - 21}[/tex][tex]\text{ y =}\frac{-5x\text{ -21}}{3}[/tex][tex]\text{ y = -}\frac{5}{3}x-7[/tex]The slope of the perpendicular line is -5/3.
Thus, for the slope of the line, we get,
[tex]\text{ m}_{\perp}\text{ = }\frac{-5}{3}[/tex][tex]\text{ m = }\frac{3}{5}[/tex]Let us solve for the value of b with the given value of slope (m) = 3/5 and (x,y) = (-5,1).
[tex]\text{ y = mx + b}[/tex][tex]1\text{ = (}\frac{3}{5})(-5)+b[/tex][tex]1\text{ = -1 + b ; b = 1 + 1 = }2[/tex]Let's now make the equation of the line using Slope-Intercept Form,
Given, m = 3/5 and b = 2
[tex]\text{ y = mx+b}[/tex][tex]\text{ y = (}\frac{3}{5})x\text{ + 2}[/tex][tex]\text{ y = }\frac{3}{5}x\text{ +2}[/tex]