Question

a line represented by y = 5x − 2 and a line perpendicular to it intersect at r(1, 3). what is the equation of the perpendicular line

Answer 1

y=ax+b, y=cx+d (a≠0, c≠0)
If the two line cross perpendicularly ⇔ ac= -1

So a tangent of the perpendicular line is "-(1/5)".

Then, the equation of the perpendicular line is y=-(1/5)x+a (a is y-intercept).

On the other hand, this equation pass r(1, 3), so

3 = -(1/5) times 1 + a

∴ a=16 / 5

Therefore, y=-(1/5)x+16 /5 is answer.

By the way, I'm Japanese so if you find some mistakes in my English, please let me know.