Use the table below to determine whether y varies directly with ×. If it does, find the constant of variation k and write the relationship as y=kx.
Please show vour work
X
3
5
6
8
y
7
11
13
19
To determine whether y varies directly with x, we need to check if the ratios of y to x are constant.
Ratio of y to x for (3,7) = 7/3 ≈ 2.33
Ratio of y to x for (5,11) = 11/5 = 2.2
Ratio of y to x for (6,13) = 13/6 ≈ 2.17
Ratio of y to x for (8,19) = 19/8 ≈ 2.375
Since the ratios are not constant, we can conclude that y does not vary directly with x.
Therefore, there is no constant of variation (k) and we cannot write the relationship as y = kx.
To determine if y varies directly with x, we need to check if the ratio of y to x is constant for each pair of values.
Let's calculate the ratios for the given values of x and y:
For x = 3, y = 7
y/x = 7/3 ≈ 2.33
For x = 5, y = 11
y/x = 11/5 = 2.20
For x = 6, y = 13
y/x = 13/6 ≈ 2.17
For x = 8, y = 19
y/x = 19/8 ≈ 2.38
Since the ratios are not the same for all the pairs, y does not vary directly with x.
Therefore, we cannot find the constant of variation (k), and we cannot write the relationship as y = kx.
To determine whether y varies directly with x, we need to check if the ratio of y to x is constant. Let's calculate the ratios for each pair of values from the table:
For x = 3, y = 7, the ratio y/x is 7/3.
For x = 5, y = 11, the ratio y/x is 11/5.
For x = 6, y = 13, the ratio y/x is 13/6.
For x = 8, y = 19, the ratio y/x is 19/8.
If these ratios are all equal, then y varies directly with x, and we can find the constant of variation, k.
Comparing the ratios:
7/3 = 11/5,
11/5 = 13/6,
13/6 ≠ 19/8.
The ratios are not all equal, so y does not vary directly with x.
Since y does not vary directly with x, we cannot find the constant of variation, k, and write the relationship as y = kx.
Therefore, there is no direct relationship between y and x in this table.