Question

for each table, determine whether it shows a direct variation. if it does, write its direct variation equation.
(table 1: x: 5, 10, 20; y: 2, 4, 8)
options: not direct variation; direct variation
equation: box
(table 2: x: 5, 10, 15; y: 8, 16, 24)
options: not direct variation; direct variation
equation: box

Explanation:

Step1: Analyze the first table

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

• \( \frac{2}{5} = 0.4 \)
• \( \frac{4}{10} = 0.4 \)
• \( \frac{8}{20} = 0.4 \)

Since \( \frac{y}{x} \) is constant (\( k = 0.4=\frac{2}{5} \)), it is direct variation. Equation: \( y=\frac{2}{5}x \)

Step2: Analyze the second table

Check \( \frac{y}{x} \) for each pair:

• \( \frac{8}{5} = 1.6 \)
• \( \frac{16}{10} = 1.6 \)
• \( \frac{24}{15} = 1.6 \)

Since \( \frac{y}{x} \) is constant (\( k = 1.6=\frac{8}{5} \)), it is direct variation. Equation: \( y=\frac{8}{5}x \)

Answer:

First table: Direct variation, Equation: \( y = \frac{2}{5}x \)
Second table: Direct variation, Equation: \( y=\frac{8}{5}x \)