Question

which of the following tables represents a function that is proportional? function 1: table of x and y values

x	y
2	4
3	6

function 2: table of x and y values

x	y
2	3
3	4

(1 point)

Explanation:

Step1: Recall Proportional Function Rule

A proportional function has the form \( y = kx \), where \( k \) is the constant of proportionality, and \( \frac{y}{x}=k \) (constant) for all \( x
eq0 \).

Step2: Check Function 1

For Function 1:

• When \( x = 1 \), \( y = 2 \), so \( \frac{y}{x}=\frac{2}{1}=2 \).
• When \( x = 2 \), \( y = 4 \), so \( \frac{y}{x}=\frac{4}{2}=2 \).
• When \( x = 3 \), \( y = 6 \), so \( \frac{y}{x}=\frac{6}{3}=2 \).

The ratio \( \frac{y}{x} \) is constant (\( k = 2 \)), so it follows \( y = 2x \), a proportional function.

Step3: Check Function 2

For Function 2:

• When \( x = 1 \), \( y = 2 \), \( \frac{y}{x}=\frac{2}{1}=2 \).
• When \( x = 2 \), \( y = 3 \), \( \frac{y}{x}=\frac{3}{2}=1.5 \).
• When \( x = 3 \), \( y = 4 \), \( \frac{y}{x}=\frac{4}{3}\approx1.33 \).

The ratio \( \frac{y}{x} \) is not constant, so it is not a proportional function.

Answer:

Function 1 (the table for Function 1: with \( x \) values 1, 2, 3 and corresponding \( y \) values 2, 4, 6) represents a proportional function.