Question

determine if the table represents a proportional relationship. show your work.

x	1	2	3	4
y	4	6	7	10

Explanation:

Step1: Recall proportional relationship rule

A proportional relationship satisfies \( \frac{y}{x}=k \) (constant) for all \( x,y
eq 0 \).

Step2: Calculate \( \frac{y}{x} \) for each pair

• For \( x = 1,y = 4 \): \( \frac{4}{1}=4 \)
• For \( x = 2,y = 6 \): \( \frac{6}{2}=3 \)
• For \( x = 3,y = 7 \): \( \frac{7}{3}\approx2.33 \)
• For \( x = 4,y = 10 \): \( \frac{10}{4}=2.5 \)

Step3: Check if \( k \) is constant

The values \( 4, 3, \frac{7}{3}, 2.5 \) are not equal.

Answer:

The table does not represent a proportional relationship.