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Part 1
For the data in the table, tell whether y varies directly with x. If it does, write an equation for the direct variation.
x
-6
1
4
y
27
-4.5
-18
Write an equation for the direct variation. Select the correct choice and fill in any answer boxes in your choice below.
A.
y
enter your response here (Use integers or decimals for any numbers in the expression.)
B.
There is no direct variation.
To determine if y varies directly with x, we can check if the ratio of y to x is constant.
When we calculate the ratios for the given values, we get:
ratio for -6 and 27: 27/-6 = -4.5
ratio for 1 and -4.5: -4.5/1 = -4.5
ratio for 4 and -18: -18/4 = -4.5
Since the ratios are all the same (-4.5), we can conclude that y varies directly with x.
To find the equation for the direct variation, we can use the formula:
y = kx
Where k is the constant of variation. We can find the value of k by substituting one of the values from the table into the equation and solving for k.
Using the value -6 for x and 27 for y:
27 = k(-6)
Solving for k:
k = 27/(-6) = -4.5
Therefore, the equation for the direct variation is:
y = -4.5x
The correct choice is A. y = -4.5x.