Proportional Relationships

1. Unit rate $= \frac{1/2}{1/4} = \frac{1}{2} \times \frac{4}{1} = 2$ miles per hour.

2. Yes, the quantities are proportional. The ratio $\frac{\text{cost}}{\text{oranges}}$ is constant:

$\frac{1.50}{2} = \frac{3.00}{4} = \frac{4.50}{6} = \frac{6.00}{8} = 0.75$

The unit rate is \0.75$ per orange.

3. The unit rate is $\frac{90}{3} = 30$ miles per gallon.

The equation is $d = 30g$.

4. | $x$ | 0 | 1 | 2 | 3 | 4 | |-----|---|---|---|---|---| | $y$ | 0 | 2.5 | 5 | 7.5 | 10 |

Yes, the graph passes through the origin $(0, 0)$, which confirms it is a proportional relationship.

5. $y = kx = 7 \times 12 = 84$.