Final answer:
The slope for option A, given by two points, is approximately 0.70, which is smaller than the absolute values for options C and D. Option C has a slope of -2, and option D has a slope of 1, meaning that -2 has the greatest absolute value for slope, while 1 is the greatest positive slope provided.
Step-by-step explanation:
To determine which of the following has the greatest slope, we analyze each option. The first two options, A and B, appear to be coordinate points, and the last two, C and D, seem to be unordered numerical pairs, possibly intended to be slope values directly.
For option A, which has points B (-7, -2) and C (10, 10), we can calculate the slope using the formula slope (m) = (y2 - y1) / (x2 - x1). Plugging in the numbers:
- m = (10 - (-2)) / (10 - (-7)) = (12) / (17) = 12/17
For options C and D, which are simply pairs of numbers, without additional context, it's not clear what these pairs represent.
Therefore, if we assume that these values represent slopes directly, we would consider option C as -2 and D as 1, in which case, option D has the greatest value among them. However, option A's slope calculation equals an approximate 0.70, which is smaller than the absolute values for both C and D, so option A's line is less steep than those represented by C and D. If directly comparing the absolute slopes, the greatest slope would be option C, as it has the largest absolute value slope of -2. But in terms of positive slope, option D would be greater.