Question

Write a two-variable linear inequality that models the graph of the solid line y=2x−4 with a shaded region above the line. Which of the following options is correct?

y<2x−4
y less than 2 x minus 4

y≤2x−4
y less-than-or-equal-to 2 x minus 4

y≥2x−4
y greater-than-or-equal-to 2 x minus 4

y>2x−4
y greater than 2 x minus 4

Answer 1

To model the graph of the solid line given by the equation \( y = 2x - 4 \) with a shaded region above the line, you need to represent the inequality that indicates the area above this line.

Since the line is solid, the value of \( y \) can be equal to \( 2x - 4 \) (which corresponds to the line itself). Therefore, the correct inequality includes the "greater than or equal to" part.

The area above the line corresponds to:

\[
y \geq 2x - 4
\]

So, the correct option is:

**y ≥ 2x - 4** (y greater than or equal to 2 x minus 4)