Question

for each table, determine whether it shows a direct variation.
if it does, write its direct variation equation.

x	y		not direct variation		x	y		not direct variation
6	3		equation:		4	10		equation:
8	12		□		6	15		□

Explanation:

Step1: Analyze the first table

For direct variation, \( y = kx \) (or \( \frac{y}{x}=k \), constant). Check ratios:

• \( \frac{1}{2} = 0.5 \)
• \( \frac{3}{6} = 0.5 \)
• \( \frac{12}{8} = 1.5 \)

Ratios are not constant, so Not direct variation.

Step2: Analyze the second table

Check \( \frac{y}{x} \):

• \( \frac{5}{2} = 2.5 \)
• \( \frac{10}{4} = 2.5 \)
• \( \frac{15}{6} = 2.5 \)

Ratio \( k = 2.5=\frac{5}{2} \), so direct variation. Equation: \( y=\frac{5}{2}x \) (or \( y = 2.5x \)).

Answer:

First table: Not direct variation
Second table: Direct variation, Equation: \( y = \frac{5}{2}x \) (or \( y = 2.5x \))