If the x intercept of the line `y = mx + 2` is greater than `1/2` then the gradient of the line lies in the interval

Options

A. (-1,0)
B. `((-1)/(4),0)`
C. `(-oo, -4)`
D. (-4,0)

Answer

D

Explanation

Given equation of line y=mx+2
`rArr (x)/(-(2)/(m))+(y)/(2) =1`
It is given that -x-intercept of the above line is greater than `(1)/(2).`
`therefore -(2)/(m) gt(1)/(2)`
`rArr -(2)/(m) -(1)/(2) gt 0`
`rArr -((4+m)/(2m)) gt 0`
`rArr (4+m)/(2m) lt 0`
`rArr -4 lt m lt 0`