Explain what defines direct variation. Then, check which of the following tables include directly proportional quantities x and y x 1 2 3 4 y 7 14 21 28
Question
Answer:
Direct variation in mathematics is when two numbers are written in an equation where one of the numbers multiplied by a constant term to equal the other. In the table in the equation, we see direct variation.
X Y
1 7
2 14
3 21
4 28
We can find the constant of the variation by dividing y by x. This constant should remain the same for all terms of x in the table with their corresponding y values.
y/x
7/1=7
14/2=7
21/3=7
28/4=7
As we can see, the values in the table all share a direct variation between x and y with the value 7.
This can be expressed in an equation: y = 7x.
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