Final answer:
To determine if the points lie on a line, we can calculate the slopes between the points and see if they are equal. If the slopes are different, the points do not lie on a line.
Step-by-step explanation:
To determine whether the points (2, 4), (4,8), and (8, 12) lie on a line, we can use the slope formula. The slope (m) between two points (x1, y1) and (x2, y2) is given by the formula m = (y2 - y1) / (x2 - x1). Let's calculate the slope between the first two points:
m = (8 - 4) / (4 - 2) = 4 / 2 = 2
Now let's calculate the slope between the second and third points:
m = (12 - 8) / (8 - 4) = 4 / 4 = 1
Since the slopes are different for the two pairs of points, these points do not lie on a line. Therefore, Ben's claim is incorrect.
Learn more about Points and slopes