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?(1 point)

Question

Responses

y<2x−4
y less than 2 x minus 4

y>2x−4
y greater than 2 x minus 4

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

y≤2x−4

Answer 1

To model the graph of the solid line \( y = 2x - 4 \) with a shaded region above the line, we need to choose an inequality that represents the area above the line. Since the line is solid, it suggests that points on the line are included in the solution.

1. The line itself can be represented by the equation \( y = 2x - 4 \).
2. The shading above the line indicates that we are interested in values of \( y \) that are greater than or equal to the values on the line.

Given these conditions, the correct inequality that represents this situation would be:

\( y \geq 2x - 4 \)

This means that the values of \( y \) can be greater than or equal to those on the line \( y = 2x - 4 \).

So, the correct option is:

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