Question

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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.

Answer 1

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.