A graphed line has a slope of 5/3
. Which of the following points could the line contain?
Question 2 options:
(15, 16) and (0, 4)
(3, 9) and (6, 14)
(0, 4) and (19, 9)
(5, 7) and (10, 10)
To determine which set of points could lie on a line with a slope of 5/3, we can calculate the slope using the formula:
slope = (change in y)/(change in x)
Let's calculate the slope for each set of points:
1) (15, 16) and (0, 4)
Change in y = 16 - 4 = 12
Change in x = 15 - 0 = 15
Slope = 12/15 = 4/5
2) (3, 9) and (6, 14)
Change in y = 14 - 9 = 5
Change in x = 6 - 3 = 3
Slope = 5/3
3) (0, 4) and (19, 9)
Change in y = 9 - 4 = 5
Change in x = 19 - 0 = 19
Slope = 5/19
4) (5, 7) and (10, 10)
Change in y = 10 - 7 = 3
Change in x = 10 - 5 = 5
Slope = 3/5
So, out of the four sets of points, the line with a slope of 5/3 could contain the points (3, 9) and (6, 14).
To determine which of the given points could lie on a line with a slope of 5/3, we need to calculate the slope between each pair of points and check if it matches 5/3.
Let's calculate the slope between the given points:
1. For (15, 16) and (0, 4):
slope = (y2 - y1) / (x2 - x1)
= (4 - 16) / (0 - 15)
= -12 / -15
= 4/5
The slope is not equal to 5/3.
2. For (3, 9) and (6, 14):
slope = (y2 - y1) / (x2 - x1)
= (14 - 9) / (6 - 3)
= 5 / 3
The slope is equal to 5/3.
3. For (0, 4) and (19, 9):
slope = (y2 - y1) / (x2 - x1)
= (9 - 4) / (19 - 0)
= 5 / 19
The slope is not equal to 5/3.
4. For (5, 7) and (10, 10):
slope = (y2 - y1) / (x2 - x1)
= (10 - 7) / (10 - 5)
= 3 / 5
The slope is not equal to 5/3.
Based on the calculations, the only pair of points that could lie on a line with a slope of 5/3 is (3, 9) and (6, 14).
To determine if a given line could contain a specific set of points, we need to verify if the slope between these points is equal to the given slope of 5/3.
Let's calculate the slope between each pair of points and check if it matches the given slope:
1. For the points (15, 16) and (0, 4), the slope is (change in y)/(change in x) = (16 - 4)/(15 - 0) = 12/15 = 4/5, which is not equal to 5/3.
2. For the points (3, 9) and (6, 14), the slope is (change in y)/(change in x) = (14 - 9)/(6 - 3) = 5/3, which matches the given slope of 5/3. Therefore, this point pair could lie on the line.
3. For the points (0, 4) and (19, 9), the slope is (change in y)/(change in x) = (9 - 4)/(19 - 0) = 5/19, which is not equal to 5/3.
4. For the points (5, 7) and (10, 10), the slope is (change in y)/(change in x) = (10 - 7)/(10 - 5) = 3/5, which is not equal to 5/3.
Therefore, the only pair of points that could lie on the line with a slope of 5/3 is (3, 9) and (6, 14).