Find an inverse variation equation that models the data. Length 4,6,8,9,10
Weight 24, 16,13,11,9
To find an inverse variation equation that models the data, we need to determine the relationship between length and weight. In an inverse variation, as one variable increases, the other decreases, and vice versa.
In this case, we can see that as the length increases, the weight decreases. This suggests an inverse relationship between length and weight.
To find the inverse variation equation, we can use the formula:
y = k/x
where y represents the weight and x represents the length. k is a constant value that needs to be determined.
Let's create a table using the given data and calculate the value of k:
Length (x) | Weight (y) | y = k/x
---------------------------------
4 | 24 | k/4 = 24
6 | 16 | k/6 = 16
8 | 13 | k/8 = 13
9 | 11 | k/9 = 11
10 | 9 | k/10 = 9
To find the value of k, we can solve the equations for k in each row.
From the first row, k/4 = 24, we can multiply both sides of the equation by 4 to get k = 96.
Using the same process for the remaining rows:
From the second row, k/6 = 16, we find k = 96.
From the third row, k/8 = 13, we find k = 104.
From the fourth row, k/9 = 11, we find k = 99.
From the fifth row, k/10 = 9, we find k = 90.
Since the values of k are different for each row, it indicates that there may be some variability in the data. To address this, we can take the average value of k across all the rows.
Average k = (96 + 96 + 104 + 99 + 90)/5 = 97
So, the inverse variation equation that models the data is:
Weight = 97/Length
Note: This is an approximation based on the given data, and the equation may not perfectly represent the relationship between length and weight.