Question

Identify the region described by the shaded part in the graph above.

• A. $y=4x-6$
• B. $y\ne 4x-6$
• C. $y<4x-6$
• D. $y>4x-6$

Answer 1

Answer: (B), (C)

The correct options are
B $y<4x-6$
C $y\ne 4x-6$

The line represents the linear equation $y=4x-6$
Any other region on the given figure represents $y\ne 4x-6$ ..$\left(i\right)$
Now writing the given equation in intercept form, we get
$4x-y=6$
$\Rightarrow \frac{x}{\frac{6}{4}}-\frac{y}{6}=1$
Therefore the line cuts the $x$-axis at $x=\frac{6}{4}$ and $y$-axis at $-6$.
Now consider an arbitrary point in the shaded region $(x,y)$ which does not lie on the line to check the inequality.
Consider point $(10,10)$
$4x-6=40-6=34$ and $y=-6$.

Hence, $y<4x-6$
Similarly, we can check the inequality for the shaded region by substituting points in that region, which do not lie on the line, and by comparing $y$ and $4x-6$
Hence, the correct answers are options B and C.