Understanding Slope Through Different Point Changes

 

I’m practicing coordinate geometry and trying to better understand how slope behaves when points change. I created the following multi-part problem and would really appreciate a clear, speed stars step-by-step explanation for each part.

Part A:

Given two points E(2, 1) and F(6, 9):

• Calculate the slope of the line passing through these points. 
• Show the formula used and explain each step clearly. 
• Describe what this slope tells us about the line (direction, steepness, increasing or decreasing). 

Part B:

Now change point F to a new position F'(6, 1):

• Find the slope of the line between E(2, 1) and F'(6, 1). 
• Compare this slope with the one from Part A. 
• Identify what type of line is formed and explain why. 

Part C:

Consider two new points G(2, 9) and H(6, 1):

• Calculate the slope between G and H. 
• Compare it with the slope from Part A in terms of sign and direction. 
• Explain what happens if both points have the same x-coordinate (for example, G(4, 9) and H(4, 1)). What kind of line is formed in that case?