Question

1. a fruit punch has a ratio of 2 cups of powder mix for every 5 gallons of water.

a. represent the ratio relationship using a graph.
b. how many cups of powder mix are used with 9 gallons of water?

Explanation:

Step1: Define proportional relationship

Let $x$ = gallons of water, $y$ = cups of powder mix. The ratio gives $\frac{y}{x} = \frac{2}{5}$, so $y = \frac{2}{5}x$.

Step2: Substitute $x=9$ into equation

Substitute the given water amount to find powder mix.
$y = \frac{2}{5} \times 9$

Step3: Calculate the value

Compute the product and simplify.
$y = \frac{18}{5} = 3.6$

For part a (graph):

This is a linear proportional relationship. Plot the points $(0,0)$ (0 gallons water needs 0 powder) and $(5,2)$ (given ratio), then draw a straight line through them extending to positive $x$ and $y$ values (since amounts can't be negative). The x-axis is labeled "Gallons of Water" and the y-axis is labeled "Cups of Powder Mix".

Answer:

a. A straight line passing through (0,0) and (5,2) on a graph with x-axis = Gallons of Water, y-axis = Cups of Powder Mix.
b. 3.6 cups (or $\frac{18}{5}$ cups)