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Use the image to answer the question.

A solid line drawn on a coordinate plane slopes steeply upward from bottom left to top right. The part of the plane to the right of the line is shaded. Both axes range from negative 10 to 10 in unit increments.

Which linear inequality matches the given graph?

(1 point)
Responses

y≥2x+2
y greater-than-or-equal-to 2 x plus 2

y<2x+2
y less than 2 x plus 2

y>2x+2
y greater than 2 x plus 2

y≤2x+2

1 answer

To determine the correct linear inequality that matches the given graph, we need to analyze the information provided:

  1. Line's Slope: The line slopes steeply upward from bottom left to top right, which indicates a positive slope. Given that the inequality options include "2x", we infer that the slope of the line is 2.

  2. Line's Position: The inequality shows the area to the right of the line is shaded. For any point (x, y) to be to the right of the line y = 2x + 2, we need y to be greater than the line itself.

  3. Boundary Line: Since the line is solid, it means that points on the line satisfy the inequality, which indicates that the inequality includes "equal to" (≥ or ≤).

Given which options are available:

  • y ≥ 2x + 2: This means y is greater than or equal to the line, which corresponds to the area above or on the line.
  • y < 2x + 2: This means y is less than the line, which corresponds to the area below the line (not shaded).
  • y > 2x + 2: This means y is greater than the line, which corresponds to above the line but does not include points on the line (not correct because the line is solid).
  • y ≤ 2x + 2: This means y is less than or equal to the line, which corresponds to below or on the line (not shaded).

Since the region to the right of the line is shaded and points on the line are included, the correct answer is:

y ≥ 2x + 2.