Write an equation, in point-slope form, for the line that is perpendicular to y – 10 = 3/2 (x – 4) and that passes through the point (4, 2).

Question

Write an equation, in point-slope form, for the line that is perpendicular to y – 10 = 3/2 (x – 4) and that passes through the point (4, 2).

My Answer:

Formula for point-slope form; y – y = m(x – x)
Insert y and x value; y – 2 = m(x – 4)
If the slope for the original line is 3/2, a perpendicular line would have a slope that is a negative reciprocal; -2/3
Therefore final equation is; y – y = -2/3(x - 4)

Am I right? Can someone please check my work?

Answer 1

y-2=-2/3 (x-4)

Answer 2

Oops, I forgot to put in the 2, my bad...Thanks! (=

Answer 3

Your work is correct! The equation you derived, y - 2 = -2/3(x - 4), is indeed in point-slope form for a line that is perpendicular to the given line y - 10 = 3/2(x - 4) and passes through the point (4, 2). Well done!