x y
1 11
8 13
9 15
10 17
Determine whether y varies directly with c. if so, find the constant of the variation k and write the equation
To determine whether y varies directly with x, we can look at the ratios of y to x for each pair of values:
For the first pair, y/x = 11/1 = 11.
For the second pair, y/x = 13/8 = 1.625.
For the third pair, y/x = 15/9 = 1.667.
For the fourth pair, y/x = 17/10 = 1.7.
Since the ratios are not the same for each pair, we can conclude that y does not vary directly with x. There is no constant of variation (k) or equation that represents the relationship between y and x.
To determine whether y varies directly with c, we need to check if the ratio of y to c is constant for all given values. Let's calculate the ratios:
For the first set: y/c = 11/1 = 11.
For the second set: y/c = 13/8 = 1.625.
For the third set: y/c = 15/9 = 1.667.
For the fourth set: y/c = 17/10 = 1.7.
Since the ratios are not constant for all sets, we can conclude that y does not vary directly with c. Therefore, there is no constant of variation (k) and there is no equation in the form y = kc.
To determine whether y varies directly with x, we need to check if the ratio between y and x remains constant. If the ratio is constant, then the relationship between y and x is direct variation.
Let's calculate the ratios between y and x for each pair of values:
For the first pair (1, 11):
y/x = 11/1 = 11
For the second pair (8, 13):
y/x = 13/8 = 1.625
For the third pair (9, 15):
y/x = 15/9 = 1.6667
For the fourth pair (10, 17):
y/x = 17/10 = 1.7
Since the ratios are not the same for all pairs, y does not vary directly with x.
If y were to vary directly with x, the ratio y/x would be constant for all pairs. However, in this case, the ratios are different, indicating a non-direct variation relationship.
Therefore, we cannot find the constant of variation (k) or write an equation for direct variation since it does not exist in this dataset.