A line has slope –The fraction negative five thirds.. Through which two points could this line pass?
(1 point)
Responses
(12, 13), (17, 10)
(12, 13), (17, 10)
(16, 15), (13, 10)
(16, 15), (13, 10)
(0, 7), (3, 10)
(0, 7), (3, 10)
(11, 13), (8, 18)
(11, 13), (8, 18)
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).