Write a two-variable linear inequality that models the graph of the solid line y=2x−4

Question

with a shaded region above the line. Which of the following options is correct?(1 point)
Responses

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

y<2x−4
y less 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, you need to use the inequality that indicates all points above this line, while also including the points on the line itself, since it is indicated by a solid line.

The correct inequality representing this situation would be:

\[ y \geq 2x - 4 \]

This means \( y \) is greater than or equal to \( 2x - 4 \), which corresponds to the shaded region above the line, including the line itself.

Thus, the correct option from your list is:

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