Question

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 ap
(-2,-5) and (-7, -3)
(-1, 1) and (-6, -1)
(0, 0) and (2, 5)
(1, 0) and (6, 2)
(3, 0) and (8, 2)

Answer 1

To determine if a line is parallel to another line, we need to check if their slopes are equal. The correct options are the first, second, fourth, and fifth options.

Step-by-step explanation:

To determine if a line is parallel to another line, we need to check if their slopes are equal.

The slope of the line containing (3, 4) and (-2, 2) is (2-4)/(-2-3) = -2/5.

Now let's check the slopes of the other lines:

1. The slope of the line containing (-2,-5) and (-7, -3) is (-3-(-5))/(-7-(-2)) = 2/5. So, the first option is correct.
2. The slope of the line containing (-1, 1) and (-6, -1) is (-1-1)/(-6-(-1)) = -2/5. So, the second option is correct.
3. The slope of the line containing (0, 0) and (2, 5) is (5-0)/(2-0) = 5/2. So, the third option is NOT correct.
4. The slope of the line containing (1, 0) and (6, 2) is (2-0)/(6-1) = 2/5. So, the fourth option is correct.
5. The slope of the line containing (3, 0) and (8, 2) is (2-0)/(8-3) = 2/5. So, the fifth option is correct.

Therefore, the correct options are the first, second, fourth, and fifth options.

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