Question

1. which relationship is a direct variation?

f

x	1	2	3	4
y	-1	0	1	2

g

x	1	2	3	4
y	0	-1	-2	-3

h

x	1	2	3	4
y	3	5	7	9

j

x	1	2	3	4
y	3	6	9	12

Explanation:

Step1: Recall Direct Variation

Direct variation has the form \( y = kx \), so \( \frac{y}{x}=k \) (constant) for all \( x
eq0 \).

Step2: Check Option F

For F: \( \frac{-1}{1}=-1 \), \( \frac{0}{2}=0 \). Not constant. Reject.

Step3: Check Option G

For G: \( \frac{0}{1}=0 \), \( \frac{-1}{2}=-0.5 \). Not constant. Reject.

Step4: Check Option H

For H: \( \frac{3}{1}=3 \), \( \frac{5}{2}=2.5 \). Not constant. Reject.

Step5: Check Option J

For J: \( \frac{3}{1}=3 \), \( \frac{6}{2}=3 \), \( \frac{9}{3}=3 \), \( \frac{12}{4}=3 \). Constant \( k = 3 \).

Answer:

J. \( \boldsymbol{x}\): 1, 2, 3, 4; \( \boldsymbol{y}\): 3, 6, 9, 12