We need to find the slope of the blue given line to determine the slope of the perpendicular bisector of this blue line.
From the graph, we see that if x increases from 2 to 4, y decreases from 4 to -2. Thus, the slope of the blue line is [-2-4] divided by 4-2, or m = -6/2, or m = -3.
The slope of the perpend. bisector of the blue line is the negative reciprocal of -3, or m= 1/3.
Let's find the slope-intercept form of this bisector. We need to determine b in y=mx+b. Referring to the midpoint of the blue line, x= 3; y= 1; and m=1/3. Then
y=mx+b becomes 1=(1/3)(3) + b. Solving for b: 1=1+b. Then b=0.
Thus, the equation of the perpendicular bisector of the blue line through (3,1) is y=mx + b, or y=(1/3)x + 0, or y=x/3.
