Question

A line L1 passes through point (1,2) and has a gradient of 5.Another line L2 is perpendicular to L1 and meets it at a point where x=4.find the equation of L2.i got L2 gradient as -5 am i right. How do i use x=4 and the equation.please help

Answer 1

No. L2 has slope -1/5
⊥ lines have slopes which are negative reciprocals

The point-slope equation of L1 is
y-2 = 5(x-1)
So, when x=4, y=17

Using the point (4,17) on L2, its equation is
y-17 = -1/5 (x-4)

Answer 2

L1: (1, 2), (4, y), m = 5.
m = (y-2)/(4-1)
5 = (y-2)/3
y-2 = 15
Y = 17.

L2: (4, 17), m = -1/5.
Y = mx+b
17 = (-1/5)4+b
b = 17+4/5 = 17.8
Y = (-1/5)x+17.8