Question

Here are four pairs of points. Which of these pairs of points lie on lines with the same slope? Use the Graphing Tool to help you decide. Then confirm your answer by actually computing the slopes.

A. (2, 3) and (4, -3)
B. (1, 1) and (4, 7)
C. (2, 4) and (5, -5)
D. (0, 3) and (3, 0)

Answer 1

Calculating the slope for each pair of points, we find that pairs A (slope = -3) and C (slope = -3) have the same slope, and therefore lie on lines with the same slope.

Step-by-step explanation:

To determine which pairs of points lie on lines with the same slope, we calculate the slope for each pair. The slope (m) is computed using the formula m = (y2 - y1) / (x2 - x1).

1. For pair A (2, 3) and (4, -3), the slope is m = (-3 - 3) / (4 - 2) = -6 / 2 = -3.
2. For pair B (1, 1) and (4, 7), the slope is m = (7 - 1) / (4 - 1) = 6 / 3 = 2.
3. For pair C (2, 4) and (5, -5), the slope is m = (-5 - 4) / (5 - 2) = -9 / 3 = -3.
4. For pair D (0, 3) and (3, 0), the slope is m = (0 - 3) / (3 - 0) = -3 / 3 = -1.

After calculating the slopes, we see that pairs A and C have the same slope of -3, indicating they lie on lines with the same slope.