Through (-3,-1) and perpendicular to y= -2/5-4

Y=5/2x+6.5 because a line perpendicular to another line has a slope that is the negative reciprocal of the line it intersects. The negative reciprocal of -2/5 is 5/2. Then you plug in the coordinate (-3, -1) in order to find the value of b in the equation y=mx+b. The equation becomes -1=5/2(-3)+b. 5/2(-3)=-15/2=-7.5. The new equation is -1=-7.5+b. To isolate b you would add 7.5 to -1 which equals 6.5, so b=6.5. Then you plug that back into the equation and you would have y=5/2x+6.5