Answer: y = 3x - 10
Explanation:
Compare the original equation to the form y = mx+b
The original line has slope -1/3. The negative reciprocal of this is 3/1 or simply 3. This represents the perpendicular slope. The original and perpendicular slopes multiply to -1.
We'll use this perpendicular slope along with the coordinates of (x,y) = (4,2) in the point-slope equation below. Solve for y.
[tex]y - y_1 = m(x - x_1)\\\\y - 2 = 3(x - 4)\\\\y - 2 = 3x - 12\\\\y = 3x - 12+2\\\\y = 3x - 10\\\\[/tex]
As a check, plugging x = 4 should lead us to y = 2
[tex]y = 3x - 10\\\\y = 3(4) - 10\\\\y = 12 - 10\\\\y = 2\\\\[/tex]
It works out. This confirms (4,2) is on the line y = 3x-10, and helps confirm the answer.
