Final answer:
To find another point on a line with a given slope and passing through a known point, one must apply the slope formula to each candidate point to see if it yields the correct slope. In this case, only the point (-2, -30) produces a slope of 7 when used with the point (3, 5), thus it is the correct answer.
Step-by-step explanation:
The question involves finding which point could be on a line that has a slope of 7 and passes through the point (3, 5). To determine which point could also be on the line, we can use the slope formula, which is the change in y divided by the change in x (rise over run) between any two points on the line. The formula is: slope (m) = (y2 - y1) / (x2 - x1).
Going through each of the given options:
For option a, (-1, -24), the slope calculation would be (-24 - 5) / (-1 - 3) = -29 / -4 = 7.25 which is not exactly 7, so this point does not lie on the line.
For option b, (-2,-30), the slope calculation would be (-30 - 5) / (-2 - 3) = -35 / -5 = 7. This point has the correct slope and could be on the line.
For option c, (6,24), the slope calculation would be (24 - 5) / (6 - 3) = 19 / 3 which does not equal 7, so this point is not on the line.
For option d, (10,55), the slope calculation would be (55 - 5) / (10 - 3) = 50 / 7 which does not equal 7, so this point also cannot be on the line.
The correct answer is option b, (-2, -30), as it is the only point that results in the required slope of 7 when paired with the original point (3, 5).