Question

Match the inequality to its graph. A. B. C. D. Question −2y > 2 (1 point) Responses A A B B C C D

Answer 1

[AI-generated answer — Bot GPT 3.5]

The match would be:

A. D

Answer 2

[AI-generated answer — Step-by-Step Bot]

The inequality -2y > 2 can be matched with response C.

Response A: This is not the correct graph as it shows a line with positive slope, whereas the inequality has a negative coefficient for y.

Response B: This is also not the correct graph as it shows a line with negative slope, but the inequality has a negative coefficient for y.

Response C: This is the correct graph as it shows a line with negative slope, representing the inequality -2y > 2.

Response D: This is not the correct graph as it shows a vertical line, whereas the inequality does not have any restrictions on x.

Answer 3

[AI-generated answer — Explain Bot]

To match the inequality to its graph, we need to solve the inequality first and then graph its solution. Let's solve the given inequality:

−2y > 2

To solve an inequality involving the variable y, we need to isolate y on one side of the inequality sign. Let's start by dividing both sides of the inequality by −2. Since we are dividing by a negative number, the inequality sign should flip.

When we divide −2y by −2, we get y on the left side of the inequality. On the right side, we have 2 divided by −2, which is −1.

y < −1

Now, we have the solution to the inequality, which states that y is less than −1. Let's graph this inequality on a number line to match it with the corresponding graph.

On a number line, we mark a point at −1 and shade the region to the left of it since the inequality states that y is less than −1. This shaded region represents all the possible values of y that satisfy the inequality.

Now, let's look at the given options:

A. The graph of inequality −2y > 2 does not match y < −1 since it shows the region to the right of −1.

B. The graph of inequality −2y > 2 does not match y < −1 since it shows the region to the right of −1.

C. The graph of inequality −2y > 2 matches y < −1 since it correctly shows the shaded region to the left of −1.

D. The graph of inequality −2y > 2 does not match y < −1 since it shows the region to the right of −1.

So, the correct match for the inequality −2y > 2 is option C.

Response: C