What is the y- intercept of the line perpendicular to y = 3/2x - 6 and passing through the point 9,-4

 which agrees with the fourth answer shown in the list

Step-by-step explanation:

The midpoint of the segment, would also be located at x = 5 (on the same vertical segment) and the vertical position would be exactly half way from the ends of the segment.

So we need to find the segment's length which is the distance between 4 and -3. that is; |4-(-3)| = 7

Now half of such length is : 3.5 units. So counting from either end of the segment 3.5 units, we should get to that midpoint. For example if we count from the top end (located at 4 in the vertical axis), we subtract 3.5 units to go down the the center of the segment, and get 4 - 3.5 = 0.5 (one half)

Then the midpoint is located at x=5 and y=0.5

The correct answer in coordinate pair form is then