To determine the correct answer, we need to use the formula for finding the slope between two points:
m = (y2 - y1)/(x2 - x1)
Given that the slope is -5/3, we can set up the equation -5/3 = (y2 - y1)/(x2 - x1) and substitute the values from each set of points to see if we get -5/3.
1. For the first set of points (12, 13) and (17, 10), we have:
-5/3 = (10 - 13)/(17 - 12) = -3/5
Since -3/5 does not equal -5/3, these points do not satisfy the given slope.
2. For the second set of points (16, 15) and (13, 10), we have:
-5/3 = (10 - 15)/(13 - 16) = 5/3
Since 5/3 is the reciprocal of -5/3, these points satisfy the given slope.
3. For the third set of points (0, 7) and (3, 10), we have:
-5/3 = (10 - 7)/(3 - 0) = 1/1 = 1
Since 1 is not equal to -5/3, these points do not satisfy the given slope.
4. For the fourth set of points (11, 13) and (8, 18), we have:
-5/3 = (18 - 13)/(8 - 11) = -5/(-3) = 5/3
Since 5/3 is equal to -5/3, these points satisfy the given slope.
Therefore, the line with a slope of -5/3 could pass through the points (16, 15) and (13, 10) or (11, 13) and (8, 18).