Question 648398
You're almost right, except for your reasoning on the slope. The midpoint of the line between (-6,10) and (2,4) is as you correctly calculated (-2,7). Your line must go through that point. The other condition is that the line is perpendicular to y=3. And as you stated this has a zero slope (a horizontal line). However, you want a line that is PERPENDICULAR to a horizontal line, and that is a VERTICAL line that has an undefined slope (because it is the negative inverse of zero). The equation of a vertical line is
(1) x = constant
And since your line must go through (-2,7), the value of that constant is the x-coordinate of that point, giving you
(2) x = -2
Answer: The equation of the line perpendicular to y=3 and passes through the point (-2,7) is x = -2
See it?