Question

1. graph this relationship. is this proportional?

hours | inches
1 | 2
2 | 3
3 | 4
4 | 5

Explanation:

Step1: Recall proportional relationship rules

A proportional relationship has a constant ratio (\( \frac{y}{x} \)) and passes through the origin \((0,0)\). Let \( x \) be hours, \( y \) be inches.

Step2: Check the ratio \( \frac{y}{x} \)

For \( (1,2) \): \( \frac{2}{1} = 2 \)
For \( (2,3) \): \( \frac{3}{2} = 1.5 \)
Ratios are not equal. Also, check if the line passes through \((0,0)\): If \( x = 0 \), from the pattern \( y = x + 1 \) (since \( 2=1+1, 3=2+1 \), etc.), so \( y = 1 \) when \( x = 0 \), not \( 0 \).

Step3: Conclude proportionality

Since the ratio \( \frac{y}{x} \) is not constant and the graph does not pass through the origin, the relationship is not proportional.

Answer:

The relationship is not proportional.