Question

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

x	y	\
---	---	\
2	5	\
4	10	\
6	21	\

\
\bigcirc not direct variation \
\bigcirc direct variation \
equation: \
\square \
\

x	y	\
---	---	\
5	4	\
15	12	\
25	20	\

\
\bigcirc not direct variation \
\bigcirc direct variation \
equation: \
\square

Explanation:

Step1: Recall direct variation definition

Direct variation means \( y = kx \) (or \( \frac{y}{x}=k \), constant). Check \( \frac{y}{x} \) for each table.

Step2: Analyze first table (x: 2,4,6; y:5,10,21)

• For \( x=2, y=5 \): \( \frac{5}{2}=2.5 \)
• For \( x=4, y=10 \): \( \frac{10}{4}=2.5 \)
• For \( x=6, y=21 \): \( \frac{21}{6}=3.5 \) (not constant). So first table: Not direct variation.

Step3: Analyze second table (x:5,15,25; y:4,12,20)

• For \( x=5, y=4 \): \( \frac{4}{5}=0.8 \)
• For \( x=15, y=12 \): \( \frac{12}{15}=0.8 \)
• For \( x=25, y=20 \): \( \frac{20}{25}=0.8 \) (constant \( k = 0.8=\frac{4}{5} \)). So second table: Direct variation, equation \( y=\frac{4}{5}x \) (or \( y = 0.8x \)).

Answer:

First table: Not direct variation
Second table: Direct variation, Equation: \( y=\frac{4}{5}x \) (or \( y = 0.8x \))