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Determining Parallel Lines
Which ordered pairs could be points on a line parallel to the line that contains (3, 4) and (-2, 2)? Check all that apply.
O (-2,-5) and (-7, -3)
0 (-1, 1) and (-6, -1)
(0, 0) and (2, 5)
(1, 0) and (6, 2)
(3, 0) and (8, 2)
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Answer 1

The ordered pairs that could be points on a line parallel to the given line are (-2, -5) and (-7, -3), (1, 0) and (6, 2), and (3, 0) and (8, 2).

Step-by-step explanation:

To determine which ordered pairs could be points on a line parallel to the line that contains (3, 4) and (-2, 2), we need to find the slope of the given line. The formula to calculate the slope is (y2 - y1) / (x2 - x1). Using the coordinates (3, 4) and (-2, 2), we get a slope of (2 - 4) / (-2 - 3) = -2 / -5 = 2/5.

Therefore, any line parallel to the given line will have the same slope of 2/5. Comparing the slopes of the possible lines in the answer choices:

• (-2,-5) and (-7, -3): The slope is ( -3 - (-5) ) / ( -7 - (-2) ) = 2/5. This pair of points satisfies the condition.
• (-1, 1) and (-6, -1): The slope is ( -1 - 1 ) / ( -6 - (-1) ) = -2/5. This pair of points does not satisfy the condition.
• (0, 0) and (2, 5): The slope is ( 5 - 0 ) / ( 2 - 0 ) = 5/2. This pair of points does not satisfy the condition.
• (1, 0) and (6, 2): The slope is ( 2 - 0 ) / ( 6 - 1 ) = 2/5. This pair of points satisfies the condition.
• (3, 0) and (8, 2): The slope is ( 2 - 0 ) / ( 8 - 3 ) = 2/5. This pair of points satisfies the condition.

From the analysis, the ordered pairs that could be points on a line parallel to the given line are (-2, -5) and (-7, -3), (1, 0) and (6, 2), and (3, 0) and (8, 2).

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