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x y
7 11
8 13
9 15
10 17
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
each difference is 2, so start with
y = 2x
Now, since 11 = 14-3, adjust things to get
y = 2x-3
Well, let's take a look at the data points you provided:
x y
7 11
8 13
9 15
10 17
To determine if y varies directly with x, we need to see if there is a constant ratio between them. Let's calculate the ratios for each data point:
11/7 = 1.57
13/8 = 1.625
15/9 ≈ 1.67
17/10 = 1.7
As you can see, the ratios are not exactly the same, which means that y does not vary directly with x. If it did, the ratios would be equal.
Therefore, we cannot find the constant of variation (k) or write an equation for direct variation in this case.
To determine whether y varies directly with x, we need to check if the ratio of y to x remains constant for all given values.
Let's calculate the ratio (y/x) for each pair of values:
For the first pair (x=7, y=11):
Ratio = y/x = 11/7 = 1.57
For the second pair (x=8, y=13):
Ratio = y/x = 13/8 = 1.625
For the third pair (x=9, y=15):
Ratio = y/x = 15/9 = 1.667
For the fourth pair (x=10, y=17):
Ratio = y/x = 17/10 = 1.7
Since the ratio (y/x) is not constant for all given values, y does not vary directly with x.
Therefore, we cannot find a constant of variation (k) or write an equation for direct variation.
To determine whether y varies directly with x, we need to check if there is a constant ratio between the values of x and y. We can do this by comparing the ratios of y to x for each pair of values.
Let's calculate the ratios:
For the first pair:
y/x = 11/7 = 1.5714
For the second pair:
y/x = 13/8 = 1.625
For the third pair:
y/x = 15/9 = 1.6667
For the fourth pair:
y/x = 17/10 = 1.7
Since the ratios are not consistent and do not have the same value, we can conclude that y does not vary directly with x.
Therefore, there is no constant of variation k and we cannot write an equation for the relationship between x and y.