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)?

y − 3 = (x + 4) < < answer this with the given information

(-4,-3)(4,1)slope formula : (y2 - y1) / (x2 - x1)
slope = (1 - (-3) / (4 - (-4) = (1 + 3) / (4 + 4) = 4/8 = 1/2

A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal of slope 1/2, we flip the slope and change the sign.
So our perpendicular line will have a slope of -2/1 or just -2 (see how I flipped 1/2, making it 2/1, and then changed the sign, making it -2/1..or just -2)

y - y1 = m(x - x1)
slope(m) = -2
(-4,3)x1 = -4 and y1 = 3
now we sub
y - 3 = -2(x - (-4) =
y - 3 = -2(x + 4) <=== ur perpendicular line