Question

Two perpendicular lines intersect on the -axis. The equation of one line is y- 4x-6=0. Determine the equation of the other line.

Answer 1

y =
`-(1)/(4)`x + 6 or y =
`-(1)/(4)`x - 0.375

Explanation:

For 2 lines to be perpendicular, their slopes must be negative reciprocals. In order to find the perpendicular of y - 4x - 6 = 0:

SLOPE INTERCEPT FORM: y = 4x + 6

SLOPE OF LINE A: m=4

SLOPE OF LINE B (the one you are looking for): m=
`-(1)/(4)`

Since I don't know if you meant that they intercept on the x or y axis I will do both.

y-axis

y-6=
`-(1)/(4)`(x-0)

y =
`-(1)/(4)`x+6

x-axis

y-0=
`-(1)/(4)`(x-1.5)

y=
`-(1)/(4)`x-0.375