A line contains the points (−4, 1) and (4, 6). Select the points below that are also on that line. [Hint: You can use your understanding of slope, or sketch a graph.]
(12, 11)
(12, 11)
(80, 50)
(80, 50)
(0, 3.5)
(0, 3.5)
(-1, 2.875)
slope = (6-1)/(4-(-4)) = 5/8
equation:
y = (5/8)x + b, with (4,6) on it, then
6 = (5/8)(4) + b
6 - 5/2 = b
b = 7/2
equation: y = (5/8)x + 7/2
now sub in the given points to see if they satisfy.
e.g. is (80,50) on it??
LS = 50
RS = (5/8)(80) + 7/2
= 50+7/2 ≠ 50
So NO, (80,50) does not lie on the line.
check the other points the same way
um i'm doing a test on this and I can't figure out what the answer is
To determine whether a point lies on a line, you can use the slope of the line and the coordinates of the point. The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Using the given points (-4, 1) and (4, 6), we can find the slope of the line:
slope = (6 - 1) / (4 - (-4))
= 5 / 8
Now, let's check which points are on the same line.
1) (12, 11):
To check if this point lies on the line, we need to calculate its slope with either of the given points (-4, 1) or (4, 6).
slope = (11 - 1) / (12 - (-4))
= 10 / 16
= 5 / 8
Since the slope of the point (12, 11) is the same as the slope of the line, this point lies on the line.
2) (80, 50):
Using the same approach:
slope = (50 - 1) / (80 - (-4))
= 49 / 84
Since the slope of the point (80, 50) does not match the slope of the line, this point does not lie on the line.
3) (0, 3.5):
Again, calculate the slope:
slope = (3.5 - 1) / (0 - (-4))
= 2.5 / 4
= 5 / 8
Since the slope of the point (0, 3.5) is the same as the slope of the line, this point lies on the line.
4) (-1, 2.875):
Calculating the slope:
slope = (2.875 - 1) / (-1 - (-4))
= 1.875 / 3
= 15 / 24
= 5 / 8
Since the slope of the point (-1, 2.875) matches the slope of the line, this point also lies on the line.
Based on the calculations, the points (12, 11), (0, 3.5), and (-1, 2.875) are all on the line passing through the points (-4, 1) and (4, 6).