Question

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

Answer 1

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.