Question

select the tables that show a proportional relationship between x and y.

x	y
2	3
3	8
4	15
x	y
1	5
2	10
3	15

Explanation:

Step1: Recall proportional relationship rule

For a proportional relationship, \( \frac{y}{x} \) must be constant (i.e., \( y = kx \) where \( k \) is the constant of proportionality).

Step2: Check first table

• For \( x = 2, y = 3 \): \( \frac{y}{x}=\frac{3}{2} = 1.5 \)
• For \( x = 3, y = 8 \): \( \frac{y}{x}=\frac{8}{3}\approx2.67 \)
• Since \( 1.5

eq2.67 \), first table is not proportional.

Step3: Check second table

• For \( x = 1, y = 5 \): \( \frac{y}{x}=\frac{5}{1}=5 \)
• For \( x = 2, y = 10 \): \( \frac{y}{x}=\frac{10}{2}=5 \)
• For \( x = 3, y = 15 \): \( \frac{y}{x}=\frac{15}{3}=5 \)
• The ratio \( \frac{y}{x} \) is constant (5), so second table is proportional.

Answer:

The table on the right (with \( x = 1,y = 5 \); \( x = 2,y = 10 \); \( x = 3,y = 15 \))