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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](https://speed-stars.co/) step-by-step explanation for each part. **Part A:** Given two points E(2, 1)…
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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](https://speed-stars.co/) 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?
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