Question

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Allel and Perpendicular Lines (Sec 3-6) Supports Target M
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.
(-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)
Done

Answer 1

To determine points on a line parallel to (3, 4) and (-2, 2), find the slope and use the point-slope formula. The potential points are (-2,-5) and (-7, -3), (0, 0) and (2,5), 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 between two points (x1, y1) and (x2, y2) is: slope = (y2 - y1) / (x2 - x1). Let's calculate the slope of the given line: slope = (2 - 4) / (-2 - 3) = -2 / -5 = 2/5. Now, we can find the equation of any line parallel to the given line by using the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Let's check each ordered pair:

1. (-2,-5) and (-7, -3): y - (-5) = (2/5)(x - (-2)) -> y + 5 = (2/5)(x + 2) -> y + 5 = (2/5)x + 4/5
2. (-1, 1) and (-6, -1): y - 1 = (2/5)(x - (-1)) -> y - 1 = (2/5)(x + 1)
3. (0, 0) and (2,5): y - 0 = (2/5)(x - 0) -> y = (2/5)x
4. (1, 0) and (6, 2): y - 0 = (2/5)(x - 1) -> y = (2/5)x - 2/5
5. (3, 0) and (8, 2): y - 0 = (2/5)(x - 3) -> y = (2/5)x - 6/5

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

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