The problem in the image asks to select the statement that is the inverse of the following conditional statement:

Original statement:
"If two lines are parallel, then they have the same slope."

Understanding the Inverse:

The inverse of a conditional statement of the form "If P, then Q" is "If not P, then not Q."
In other words, for the given statement:

• P: "Two lines are parallel."
• Q: "They have the same slope."

So, the inverse is:
"If two lines are not parallel, then they do not have the same slope."

Answer Analysis:

Let's review the answer options:

1. "If two lines are parallel, then they don't have the same slope."
   This is incorrect because it's the opposite of the original statement.

2. "If two lines aren't parallel, then they don't have the same slope."
   This matches the inverse. It is the correct answer.

3. "If two lines have the same slope, then they are parallel."
   This is the converse of the original statement, not the inverse.

4. "If two lines don't have the same slope, then they aren't parallel."
   This is logically correct but represents the contrapositive of the original statement, not the inverse.

Correct answer:

Option 2: "If two lines aren't parallel, then they don't have the same slope."

Would you like further details or explanations?
Here are 5 related questions to expand your understanding:

1. What is the converse of a conditional statement?
2. How do you find the contrapositive of a statement?
3. Can two lines have the same slope but not be parallel?
4. What is the difference between converse and inverse in logic?
5. What are the key conditions for two lines to be parallel?

Tip: Always remember, the inverse of a statement switches both the hypothesis and conclusion to their negations without swapping their positions!