Question

Select all that apply.

Which representations show a direct variation?

y = - x

y = 2 x + 3

Input (x) 3 6 9 12 15
Output (y) 4 8 12 16 20

Answer 1

• Options 1 and 3 are direct variation

Explanation:

Direct variation is:

• y = kx

Options:

1.

• y = -x, k = -1, yes

2.

• y = 2x + 3, not a direct variation, no

3.

Try the input/output to determine the direct variation:

• 4 = 3k
• k = 4/3

Verify the other pairs:

• x = 6, y = 6(4/3) = 8
• x = 9, y = 9(4/3) = 12
• x = 12, y = 12(4/3) = 16
• x = 15, y = 15(4/3) = 20

This is also a direct variation