For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.
X,Y
8 13
16 26
24 39
A. yes; y = 5x
B. yes; y = 10x
C. yes; y = 1.625x ***
D. no; y does not vary directly with x.
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To determine if y varies directly with x, we can compare the ratios of y to x for each pair of values given in the table.
Let's calculate these ratios:
For the first pair (x=8, y=13), the ratio is y/x = 13/8 ≈ 1.625.
For the second pair (x=16, y=26), the ratio is y/x = 26/16 = 1.625.
For the third pair (x=24, y=39), the ratio is y/x = 39/24 ≈ 1.625.
Since all the ratios are the same (approximately 1.625), we can conclude that y varies directly with x.
Now, let's write the equation for the direct variation. The equation will have the form y = kx, where k represents the constant of variation. To find the value of k, we can use any of the pairs of values given in the table. Let's use the first pair (x=8, y=13):
13 = k * 8
To solve for k, divide both sides of the equation by 8:
k = 13/8 = 1.625
Therefore, the equation for the direct variation is y = 1.625x.
So, the correct answer is C. yes; y = 1.625x.