Determine If The Tables And Graph Below Express A Direct Variation Between…

Determine if the tables and graph below express a direct variation between the variables or not. If they do, find the constant of variation and an equation that defines the relation.

Determine if the tables and graph below express a direct variation between the variables or not. If they do, find the constant of variation and an equation that defines the relation.

The values of the table must be equal to each other as per equation k = y/x to show that the table is a constant of variation. If the values are not equal, then it is not a direct variation.

1.)

k = constant of variation

y = kx

k = y/x

6/2 = 12/4 = 18/6 = 24/8

3   =    3   =    3   =    3

Yes, they express  a direct variation with k = 3.

The equation formed is  y = 3x

2.)

k = constant of variation

y = kx

k = y/x

8/12 = 10/8 = 12/4 = 16/2

2/3  ≠   5/4 ≠   3    ≠   8

No, this is not a direct variation because the constant values are not equal

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