If `P` is a point `(x ,y)` on the line `y=-3x` such that `P` and the point (3, 4) are on the opposite sides of the line `3x-4y=8,` then `x >8/(15)` (b) `x >8/5` `y<-8/5` (d) `y<-8/(15)`

Options

A. `x gt 8//15`
B. `x gt 8//5`
C. `x lt -8//5`
D. `y lt -8//15`

Answer

A, C

Explanation

Let L=3x-4y-8. Then the value of L at (3,4) is `3 xx 3-4 xx 4-8 = -15 lt 0.` Hence, for the point P(x,y), we should have
`L lt 0`
`"or " 3x-4y-8 gt 0`
`"or " 3x-4(-3x)-8 gt 0 " " [because P(x,y) " lies on "y = -3x]`
`"or " x gt (8)/(15)`
`"and " -y-4y-8 gt 0`
`"or " y lt -(8)/(5)`