Use the image to answer the question.

Question

A straight line and a point are plotted on a coordinate plane. The line slopes upward from left to right, starting in quadrant 3 and rising through quadrant 1. The area to the right of the line is shaded, the majority of which is in quadrants 1 and 4.

Which equation matches the inequality in the given graph?

Option #1: y<3/2x+3

Option #2: y≤3/2x+3

Option #3: y>3/2x+3

Option #4: y≥3/2x+3

(1 point)
The equation that matches the graph is Option #
.

Answer 1

To determine which inequality matches the graph described, we should consider the characteristics of the line and the shading.

1. The line slopes upward from left to right, indicating that the slope is positive.
2. The area to the right of the line is shaded, which suggests that the inequality should represent y-values above the line.

Now we can analyze the options:

• Option #1: y < 3/2x + 3 (represents all points below the line, therefore not matching the shaded area)
• Option #2: y ≤ 3/2x + 3 (also includes points on the line and those below it, not matching the shaded area)
• Option #3: y > 3/2x + 3 (represents points above the line, matching the shaded area)
• Option #4: y ≥ 3/2x + 3 (includes points on and above the line, also matching but we need to confirm if the line is solid or dashed)

Given that the area to the right of the line is shaded, the most suitable option would be Option #3: y > 3/2x + 3.

Therefore, the equation that matches the graph is Option #3.