Which of the following statements is true regarding the points (2, 3), (4, 5), a

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Question: Which of the following statements is true regarding the points (2, 3), (4, 5), and (6, 7)?

Options:

Correct Answer: They are collinear

Solution:

The slope between any two pairs of these points is the same (1), indicating they are collinear.

Which of the following statements is true regarding the points (2, 3), (4, 5), and (6, 7)?

Which of the following statements is true regarding the points (2, 3), (4, 5), and (6, 7)?

Step 1: Identify the points given: (2, 3), (4, 5), and (6, 7).
Step 2: Understand that the slope between two points can be calculated using the formula: slope = (y2 - y1) / (x2 - x1).
Step 3: Calculate the slope between the first two points (2, 3) and (4, 5).
Step 4: Using the formula, plug in the values: slope = (5 - 3) / (4 - 2) = 2 / 2 = 1.
Step 5: Now calculate the slope between the second two points (4, 5) and (6, 7).
Step 6: Again using the formula: slope = (7 - 5) / (6 - 4) = 2 / 2 = 1.
Step 7: Finally, calculate the slope between the first and last points (2, 3) and (6, 7).
Step 8: Using the formula: slope = (7 - 3) / (6 - 2) = 4 / 4 = 1.
Step 9: Since the slope between all pairs of points is the same (1), this means the points are collinear.

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