two lines are perpendicular if have the inverted slope and different sign
first find the slope of the drawn line using the formula of the slope
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \end{gathered}[/tex]i will use the points (-2,5) and (0,-3)
[tex]\begin{gathered} m=\frac{-3-5}{0-(-2)} \\ \\ m=-4 \end{gathered}[/tex]the slope of the drawn line is -4 so the slope of the perpendicular line is 1/4
finding the perpendicular line
the general equation of the line is
[tex]y=mx+b[/tex]where m is the slope and b the y-intercept
replacing the slope m=1/4 and the point (-4,-3) i can find b
[tex]\begin{gathered} (-3)=(\frac{1}{4})(-4)+b \\ -3=-1+b \\ b=-3+1 \\ b=-2 \end{gathered}[/tex]the equation of the perpendicular line is
[tex]y=\frac{1}{4}x-2[/tex]and the point-slope form is
[tex](y+3)=\frac{1}{4}(x+4)[/tex]so, the solution is the option C
