[tex]\begin{gathered} \text{ The equation that goes through a point }(x_1,y_1)\text{ is} \\ y-y_1=m(x-x_1)_{} \end{gathered}[/tex][tex]\begin{gathered} \text{if we have a line }y=mx+b \\ \text{then the slope of the perpendicular line to the first satisfy nm=-1} \\ \\ \text{the initial line is y=-2x+5} \\ n(-2)=-1 \\ n=\frac{-1}{-2} \\ n=\frac{1}{2} \\ \text{Thus the new line is of the form} \\ \\ y=\frac{1}{2}x+b \\ \\ \text{ if it passes through the point (-4,1) then} \\ 1=\frac{1}{2}(-4)+b \\ 1=-2+b \\ 3=b \end{gathered}[/tex][tex]y=\frac{1}{2}x+3[/tex]
