To determine whether y varies directly with x, we need to see if there is a constant ratio between the corresponding values of x and y.
First, we can calculate the ratio between consecutive values of x and y:
For the first pair of values (4, 6.4):
Ratio = y/x = 6.4/4 = 1.6
For the second pair of values (7, 11.2):
Ratio = y/x = 11.2/7 = 1.6
For the third pair of values (10, 16):
Ratio = y/x = 16/10 = 1.6
For the fourth pair of values (13, 20.8):
Ratio = y/x = 20.8/13 = 1.6
In each case, we have the same ratio of 1.6. This indicates that y varies directly with x.
To find the constant variation k, we can choose any pair of values and divide y by x. Let's use the first pair of values:
k = y/x = 6.4/4 = 1.6
Therefore, the constant variation is k = 1.6.
The equation that represents the direct variation is:
y = kx
Substituting the value of k, we have:
y = 1.6x
Enter your answer and show all the steps that you use to solve this problem in the space provided.
x: 4, 7, 10, 13
y: 6.4, 11.2, 16, 20.8
Determine whether y varies directly with x. If so, find the constant variation k and write the equation.
1 answer