Determine whether the variable y varies directly with x.
x y
-1 -3
0 3
1 9
2 15
3 21
4 27
a) Yes, y does vary directly with x.
b) No, y does not vary directly with x.
To determine whether the variable y varies directly with x, we need to check if the ratio between the values of y and x remains constant. Let's calculate the ratio for each pair:
-1/-3 = 1/3
0/3 = 0
1/9 ≈ 0.111
2/15 ≈ 0.133
3/21 ≈ 0.143
4/27 ≈ 0.148
Since the ratios are not constant, we can conclude that the variable y does not vary directly with x. Therefore, the correct answer is b) No, y does not vary directly with x.
To determine whether the variable y varies directly with x, we need to check if there is a constant ratio between the values of y and x. In other words, if we can multiply x by a constant number to get y, then y varies directly with x.
To check this, we can calculate the ratio between the values of y and x for each pair of values. Let's calculate the ratios:
For the first pair (-1, -3):
Ratio = y / x = -3 / -1 = 3
For the second pair (0, 3):
Ratio = y / x = 3 / 0 = undefined
For the third pair (1, 9):
Ratio = y / x = 9 / 1 = 9
For the fourth pair (2, 15):
Ratio = y / x = 15 / 2 = 7.5
For the fifth pair (3, 21):
Ratio = y / x = 21 / 3 = 7
For the sixth pair (4, 27):
Ratio = y / x = 27 / 4 = 6.75
Since the ratios are not constant for all the values of x and y, we can conclude that y does not vary directly with x. Therefore, the correct answer is b) No, y does not vary directly with x.
To determine whether the variable y varies directly with x, we need to check if the ratios between the values of y and x are constant.
Let's calculate the ratios of y to x:
For x = -1, y = -3, the ratio is y/x = -3/(-1) = 3.
For x = 0, y = 3, the ratio is y/x = 3/0 = undefined.
For x = 1, y = 9, the ratio is y/x = 9/1 = 9.
For x = 2, y = 15, the ratio is y/x = 15/2 = 7.5.
For x = 3, y = 21, the ratio is y/x = 21/3 = 7.
For x = 4, y = 27, the ratio is y/x = 27/4 = 6.75.
Since the ratios are not constant, we can conclude that y does not vary directly with x.
Therefore, the correct answer is b) No, y does not vary directly with x.