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 less than 2 x plus 2

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

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

y≤2x+2

Answer 1

To determine which linear inequality matches the given graph, we can analyze the slope and intercept of the line.

1. Steeply Upward Slope: Since the line slopes steeply upward from the bottom left to the top right, its slope is positive. The given options with the form "y >" or "y ≥" will be considered since the shaded area is above the line.

2. Testing the Equation: The equation of the line appears to be in the form \( y = 2x + 2 \). To match this with the options, we must note:

   • \( y < 2x + 2 \) indicates the region below the line.
   • \( y = 2x + 2 \) is the actual line.
   • \( y > 2x + 2 \) indicates the region above the line.

3. Shaded Area: The problem states that the area to the right of the line is shaded. Therefore, it's indicative of being above the line, which means we are looking for a "greater than" inequality.

Conclusion: The best fit for the graph as described would be: y > 2x + 2.

Therefore, the response is: y > 2x + 2.