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)
The correct answer is:
(12, 13), (17, 10)
This is because the slope of a line is determined by the difference in the y-coordinates divided by the difference in the x-coordinates between two points on the line. In this case, the slope is negative five thirds, which means that the line goes downwards from left to right.
If you calculate the slope using the given points, you will find that it is indeed negative five thirds:
Slope = (10 - 13)/(17 - 12) = -3/5
Therefore, the line with a slope of negative five thirds passes through the points (12, 13) and (17, 10).
To find two points through which the line with slope -5/3 could pass, we need to remember that the slope of a line is the difference in the y-coordinates divided by the difference in the x-coordinates for any two points on the line.
Let's consider the points (12, 13) and (17, 10):
The difference in the y-coordinates is 10 - 13 = -3.
The difference in the x-coordinates is 17 - 12 = 5.
So, the slope between these two points is (-3)/(5) = -3/5.
This doesn't match the given slope of -5/3, so these points do not work.
Let's try another set of points, (16, 15) and (13, 10):
The difference in the y-coordinates is 10 - 15 = -5.
The difference in the x-coordinates is 13 - 16 = -3.
So, the slope between these two points is (-5)/(-3) = 5/3.
This matches the given slope of -5/3, so these points do work.
Therefore, the line with slope -5/3 could pass through points (16, 15) and (13, 10).