Match the inequality to the graph.(4 points)

Question

y ≤ ax + b
y <ax + b
y > ax + b
y ≥ax + b

a. dotted line going through (-5,-5) and (5,5) and upper left half highlighted red
b. dotted line going through (-5,-5) and (5,5) and bottom right half highlighted red
c. line going through (-5,-5) and (5,5) and bottom right half highlighted red
d. line going through (-5,-5) and (5,5) and upper left half highlighted red

Answer 1

To match the inequalities with their corresponding graphs, let's analyze what each inequality represents:

1. y ≤ ax + b: This inequality includes the line (solid line) and the region below it. The graph would be a solid line with the area below it highlighted red.

2. y < ax + b: This inequality does not include the line (dotted line) and the area below it is highlighted red. The graph would be a dotted line with the area below it shaded.

3. y > ax + b: This inequality does not include the line (dotted line) and the area above it is highlighted red. The graph would be a dotted line with the area above it shaded.

4. y ≥ ax + b: This inequality includes the line (solid line) and the area above it is highlighted red. The graph would be a solid line with the area above it shaded.

Now, let's match these descriptions with the graphs provided:

• a: Dotted line going through (-5,-5) and (5,5) with upper left half highlighted red. This matches y < ax + b.
• b: Dotted line going through (-5,-5) and (5,5) with bottom right half highlighted red. This matches y > ax + b.
• c: Solid line going through (-5,-5) and (5,5) with bottom right half highlighted red. This matches y ≤ ax + b.
• d: Solid line going through (-5,-5) and (5,5) with upper left half highlighted red. This matches y ≥ ax + b.

So the matches would be:

• y ≤ ax + b: c
• y < ax + b: a
• y > ax + b: b
• y ≥ ax + b: d