Question

which table shows direct variation?

x	-2	-1	4	8
y	-4	-8	2	1
x	-29	-12	15	23
y	-29	-12	15	23

Explanation:

Step1: Recall direct variation rule

Direct variation follows $y = kx$, so $\frac{y}{x} = k$ (constant) for all non-zero $x$.

Step2: Check first table

Calculate $\frac{y}{x}$ for each pair:
$\frac{-4}{-2}=2$, $\frac{-8}{-1}=8$, $\frac{2}{4}=0.5$, $\frac{1}{8}=0.125$.
Values are not constant.

Step3: Check second table

Calculate $\frac{y}{x}$ for each pair:
$\frac{-29}{-29}=1$, $\frac{-12}{-12}=1$, $\frac{15}{15}=1$, $\frac{23}{23}=1$.
Values are constant ($k=1$).

Answer:

The second table (with x-values -29, -12, 15, 23 and matching y-values -29, -12, 15, 23) shows direct variation.