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 y varies directly with x, we can check if the ratio of y to x is constant for each pair of values.
For the given values:
-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 ratio of y to x is not constant for each pair of values, we can conclude that y does not 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 there is a constant ratio between the values of y and x. We can do this by comparing the ratios of y to x for each pair of values.
Let's calculate the ratios for each pair of values:
For the first pair (-1, -3), the ratio is -3 / -1 = 3.
For the second pair (0, 3), the ratio is 3 / 0 = undefined.
For the third pair (1, 9), the ratio is 9 / 1 = 9.
For the fourth pair (2, 15), the ratio is 15 / 2 = 7.5.
For the fifth pair (3, 21), the ratio is 21 / 3 = 7.
For the sixth pair (4, 27), the ratio is 27 / 4 = 6.75.
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 multiply x by a constant number, does the corresponding y also get multiplied by the same constant number?
To do this, let's examine the given data points:
x y
-1 -3
0 3
1 9
2 15
3 21
4 27
If we calculate the ratio of y to x for each data point, we get:
-3/(-1) = 3
3/0 (undefined because we cannot divide by zero)
9/1 = 9
15/2 = 7.5
21/3 = 7
27/4 = 6.75
Since the ratios for y and x are not the same for each data point, 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.