Final answer:
To find out which points lie on the line passing through (-9, -3) and (6,2), we calculate the slope of the line and compare it with the slope formed by each of the given points with one of the original points. The slope must be 1/3 to ensure they are on the same line; only point (b) (0, 0) meets the criteria.
Step-by-step explanation:
To determine which points lie on the same line as the one passing through the given points ( – 9, – 3) and (6,2), we need to calculate the slope of the line and check if the other points have the same slope when paired with one of the given points.
First, let's calculate the slope of the line passing through ( – 9, – 3) and (6,2):
Slope (m) = (y2 - y1) / (x2 - x1) = (2 - ( – 3)) / (6 - ( – 9)) = 5 / 15 = 1 / 3.
Now the slope between each of the given points (a, b, c, d) and one of the original points must also be 1 / 3 to ensure they are on the same line.
For point (a) (-5, -1), let's calculate the slope with (-9, -3):
Slope = (-1 - ( – 3)) / (-5 - ( – 9)) = 2 / 4 = 1 / 2, which is not equal to 1 / 3, so point (a) does not lie on the same line.
Similarly, for point (b) (0, 0), the slope with (-9, -3) is:
Slope = (0 - ( – 3)) / (0 - ( – 9)) = 3 / 9 = 1 / 3, so point (b) lies on the same line.
We will apply this same process for points (c) (3, 1) and (d) (8, 4), and if their slopes are also 1 / 3 when calculated with either of the original points, those points lie on the same line as well.