The problem asks us to determine if the table of values is proportional or not. The table contains two rows of values. The top row represents $x$ values and the bottom row represents $y$ values. The table is: $x$: 4, 7, 10 $y$: 9, 15.75, 22.5

AlgebraProportionalityRatioLinear Relationships
2025/4/16

1. Problem Description

The problem asks us to determine if the table of values is proportional or not. The table contains two rows of values. The top row represents xx values and the bottom row represents yy values. The table is:
xx: 4, 7, 10
yy: 9, 15.75, 22.5

2. Solution Steps

A table is proportional if the ratio of yy to xx is the same for each pair of values. We need to calculate yx\frac{y}{x} for each pair of values.
For the first pair:
yx=94=2.25\frac{y}{x} = \frac{9}{4} = 2.25
For the second pair:
yx=15.757=2.25\frac{y}{x} = \frac{15.75}{7} = 2.25
For the third pair:
yx=22.510=2.25\frac{y}{x} = \frac{22.5}{10} = 2.25
Since the ratio yx\frac{y}{x} is the same for all three pairs of values, the table is proportional.

3. Final Answer

Proportional

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