A line has a slope of -3/5. Through which two points could this line pass?
A. (-4, -1) and (3,20)
B. (8,1) and (13,4)
C. (-16, -4) and (12,8)
D. (-5,9) and (10,0)
To check if a line can pass through two points with a given slope, we can calculate the slope between the two points and see if it matches the given slope.
Using the slope formula: slope = (y2 - y1) / (x2 - x1)
Let's calculate the slope for each pair of given points:
A. (-4, -1) and (3,20):
slope = (20 - (-1)) / (3 - (-4)) = 21 / 7 = 3
The slope for points A is 3, not -3/5.
B. (8,1) and (13,4):
slope = (4 - 1) / (13 - 8) = 3 / 5
The slope for points B is 3/5, which matches the given slope of -3/5.
C. (-16, -4) and (12,8):
slope = (8 - (-4)) / (12 - (-16)) = 12 / 28 = 3 / 7
The slope for points C is 3/7, not -3/5.
D. (-5,9) and (10,0):
slope = (0 - 9) / (10 - (-5)) = -9 / 15 = -3 / 5
The slope for points D is -3/5, which matches the given slope of -3/5.
Therefore, the line can pass through points B and D.