Question

Determine the equation for a line perpendicular to y=1/3+4 and has an x-intercept of 2.

Answer 1

y = -3x + 6

Explanation:

Any line perpendicular to

y = (1/3)x + 4

has a slope of -1/(1/3) = -3

and equation

y = -3x + b .................(1)

If the line has an x intercept of 2 at (0,2), then

0 = -3(2) + b

solving

b = 6

By substituting b=6 into (1), the line required

y = -3x + 6

Answer 2

y = -3x + 2

Explanation:

y=
`(1)/(3)x +4`

Slope
`m_(1)=(1)/(3)`

slope of the perpendicular line
`m_(2)` =
`(-1)/(m_(1))` =
`(-1)/((1)/(3))=-1*(3)/(1)=-3\\`

b= 2

Slope intercept form of required line: y = mx + b

y = -3x + 2