The Concept of Slope – Multi-Part Math Question

 

I'm currently reviewing algebra concepts, and I'm having trouble fully understanding the idea of slope and how to apply it in different situations. I’ve come up with a multi-part question below and would appreciate a detailed explanation for each part. Please help me break it down step-by-step so I can learn how to approach these kinds of problems on my own.

Part A:

Given the two points A(3, -2) and B(7, 4),

Find the slope of the line that passes through these two points.

Explain the formula for calculating Slope 2 and show each step in detail.

Describe in words what the slope value represents in this case (e.g., direction, steepness, positive/negative, etc.).

Part B:

Suppose point B is moved to a new position, B'(7, -2).

What is the new slope of the line between A(3, -2) and B'(7, -2)?

How does this new slope compare to the one in Part A?

What kind of line is formed in this case (e.g., horizontal, vertical, diagonal)? Please explain why.

Part C:

Now try switching the y-values of the two original points:

Let’s use C(3, 4) and D(7, -2).

Calculate the slope between these new points.

How does this slope compare in value and direction to the original slope between A and B?

What would happen to the slope if both x-values were the same instead (e.g., C(5, 4) and D(5, -2))? What kind of line would that create?