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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 less than 2 x plus 2

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

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

y≤2x+2
y less-than-or-equal-to 2 x plus 2
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1 answer

To determine which linear inequality matches the given graph, we can analyze the features of the information provided.

  1. Slope of the Line: The line slopes steeply upward from bottom left to top right. This indicates that the line has a positive slope. The slope in the options appears to be 2.

  2. Position of the Shaded Area: The problem states that the area to the right of the line is shaded. In terms of inequalities, this typically means the inequality is either "greater than" or "greater than or equal to," since the shaded region represents values above the line.

  3. Solid Line: The line is solid, which implies it includes the line in the solutions. Therefore, the inequality must be "greater than or equal to" or "less than or equal to."

Given this analysis:

  • Since we are concerned with the area to the right of the line (above the line), the correct inequalities would be of the form:
    • y ≥ 2x + 2 (the region above the line including the line itself)
    • y > 2x + 2 (the region above the line, but not including the line)

However, since the line is solid, this eliminates the option "y > 2x + 2."

Therefore, the correct choice is:

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