Question

The given line passes through the points (−4, −3) and (4, 1).

Answer 1

Y − 3 =  (x + 4)

The given line passes through the points (−4, −3) and (4, 1).

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, 3)? 

Answer 2

The first thing you have to do is find the slope of the line connecting these 2 points. Use the slope formula for that: m = y2-y1/x2-x1. We do this math:
m=1-(-3)/4-(-4) to get a slope of 1/2.  We know that the line perpendicular to the one we have has to have a slope that is the opposite reciprocal of this slope which is -2.  Write the equation of the line now using that slope of -2. You only have to use 1 of the coordinates to write the equation. Let's use (4,1) cuz I'm not a fan of negative numbers. y - y1 = m(x - x1) is the formula for the equation in point-slope form. y - 1 = -2(x - 4) is the equation. That is leaving it in point-slope form. If you simplify it to slope-intercept, or y = mx + b, it would look like this: y = -2x + 9