[Solved] Mathematics – Geometry help solve geometry homework

Assignment Prompt & Instructions

[>Geometry homework help](https://www.sweetstudy.com/fields/mathematics-geometry)

I’m currently studying basic algebra and trying to get a clearer understanding of  and how it works in different situations. To practice, I’ve created a set of questions below. I’d like a detailed, step-by-step explanation for each part so I can learn how to solve similar problems on my own.

### **Part A**

Given two points:

A(3, −2) and B(7, 4)

– Find the slope of the line passing through these points.
– Clearly explain the slope formula and show each step of the calculation.
– Describe what the slope means in this situation (for example: whether it is positive or negative, how steep the line is, and what direction it moves).

### **Part B**

Now suppose point B changes position to B′(7, −2).

– Calculate the new slope of the line connecting A(3, −2) and B′(7, −2).
– Compare this slope to the one found in Part A.
– Identify the type of line formed (horizontal, vertical, or diagonal) and explain your reasoning.

### **Part C**

Next, consider switching the y-values of the original points:

C(3, 4) and D(7, −2)

– Find the slope between these two new points.
– Compare this slope to the original slope from Part A in terms of value and direction.
– Finally, explain what happens if both points have the same x-value (for example: C(5, 4) and D(5, −2)). What kind of line would this produce, and why?

I’m hoping to better understand how slope behaves under different conditions and how to recognize patterns when working with linear equations.