Question

A line has a slope of:

A. (-8, 8) and (2, 2)
B. (5,-1) and (0, 2)
C. (-3,6) and (6, -9)
D. (-2,1) and (3, -2)
E. (0, 2) and (5, 5)
Which ordered pairs could be points on a parallel line? Select two options.

Answer 1

Options B and D, which consist of the point pairs (5,-1) and (0,2), and (-2,1) and (3,-2) respectively, have the same slope of -0.6 as the reference line, indicating that they could be points on parallel lines.

Step-by-step explanation:

To determine which ordered pairs could be points on a line parallel to another, we need to find pairs that have the same slope as the original line. For a line with slope of (-8, 8) and (2, 2), we calculate the slope by taking the difference in the y-coordinates and dividing it by the difference in the x-coordinates:

Slope (m) = (y2 - y1) / (x2 - x1)

The slope of the reference line is therefore (2 - 8) / (2 - (-8)) = -6 / 10 = -0.6. Now let's check each pair:

• B. (5,-1) and (0, 2): Slope = (2 - (-1)) / (0 - 5) = 3 / -5 = -0.6. This line has a slope of -0.6, so it is parallel to the reference line.
• D. (-2,1) and (3, -2): Slope = (-2 - 1) / (3 - (-2)) = -3 / 5 = -0.6. This line also has a slope of -0.6 and is parallel to the reference line.

Options B and D have the same slope as the reference line, so the ordered pairs from these options could be points on a line parallel to the reference line.