Question

If the inequality y < 3x – 4 is graphed in the xy - plane above, which quadrant contains no solutions to the inequality? (A) Quadrant I (B) Quadrant II (C) Quadrant III (D) Quadrant IV 32

Answer 1

`\begin{gathered} The\text{ inequality is,} \\ y<3x-4 \\ \text{Make ithis equation as equality equation} \\ y=3x-4 \\ \text{Substitute x=0} \\ y=3*0-4 \\ y=-4 \\ So,\text{ the point is (0,-4)} \\ \text{Now, substitute y=0} \\ 0=3x-4 \\ x=(4)/(3) \\ so,\text{ the point is,} \\ ((4)/(3),0) \\ So\text{ the }line\text{ passes through the }(0,-4),and((4)/(3),0)_{} \\ (0,-4)\Rightarrow IV\text{ quardent} \\ ((4)/(3),0)\Rightarrow I\text{ quardent} \\ \text{If we extend this line it will passes through also II quardent} \\ So,\text{ the only III quardent does not have solution.} \\ \text{Thus, the option (C) is correct.} \end{gathered}`