Use the image to answer the question.

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-or-equal-to 2 x plus 2

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

y>2x+2

Answer 1

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

1. The line slopes steeply upward from bottom left to top right. This indicates a positive slope.
2. The part of the plane to the right of the line is shaded, meaning the values above the line satisfy the inequality.

Given that the line is described as having a slope of 2 (from the equations), we can express this line in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. The line can be expressed as \( y = 2x + 2 \).

Since the region to the right of the line is shaded, this indicates that we want the values of \( y \) that are greater than or equal to the line:

1. The line itself is included (solid line indicates "equal to"), so we use “greater than or equal to”.
2. This gives us the inequality \( y \geq 2x + 2 \).

Thus, the correct response is:

y ≥ 2x + 2.