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.
To determine if y varies directly with x, we need to check if the ratios of corresponding elements in the two sets are the same for all elements. Let's calculate the ratios:
x: 4, 7, 10, 13
y: 6.4, 11.2, 16, 20.8
The ratio for the first pair is:
6.4/4 = 1.6
The ratio for the second pair is:
11.2/7 ≈ 1.6
The ratio for the third pair is:
16/10 = 1.6
The ratio for the fourth pair is:
20.8/13 ≈ 1.6
Since the ratios are the same for all elements, we can conclude that y varies directly with x. The constant of variation, k, is the common ratio. In this case, k is approximately 1.6.
The equation of variation is y = kx. Substituting the value of k, the equation becomes:
y = 1.6x
To determine whether y varies directly with x, we need to check if there is a constant ratio between the y-values and the x-values. Let's calculate the ratios for the given x and y values:
For the first pair:
x = 4, y = 6.4
Ratio = y/x = 6.4/4 = 1.6
For the second pair:
x = 7, y = 11.2
Ratio = y/x = 11.2/7 = 1.6
For the third pair:
x = 10, y = 16
Ratio = y/x = 16/10 = 1.6
For the fourth pair:
x = 13, y = 20.8
Ratio = y/x = 20.8/13 = 1.6
Since the ratio is the same for all pairs, we can conclude that y varies directly with x.
The constant variation, k, can be found by calculating the ratio:
k = y/x = 6.4/4 = 1.6
Therefore, the equation that represents the direct variation is:
y = kx
y = 1.6x