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<32x+3


Option #2: y≤32x+3


Option #3: y>32x+3


Option #4: y≥32x+3


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

Answer 1

To determine the correct inequality that matches the graph you described, we need to focus on the properties of the line and the shading.

1. The line you mentioned slopes upward from left to right, which suggests the form y = mx + b, where m is a positive slope (in this case, it looks like the slope is 32).
2. The area to the right of the line is shaded. This indicates that the values of y are greater than the values on the line for the points in the shaded area.

Given these points:

• Since the shaded area is above the line, we are looking for an inequality that describes y values that are greater than (or possibly greater than or equal to) the line.

The options are:

• Option #1: y < 32x + 3 (This would shade below the line)
• Option #2: y ≤ 32x + 3 (This would shade below or on the line)
• Option #3: y > 32x + 3 (This would shade above the line)
• Option #4: y ≥ 32x + 3 (This would shade above or on the line)

Since the shaded area is above the line, the correct choice would be Option #3: y > 32x + 3.

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