Maria made two batches of fruit punch. The table at the right shows how many quarts of juice she used for each batch. Write an equation that relates the proportional quantities. Convince Me! How does the equation change if the amount of grape juice is the independent variable, x, and the amount of apple juice is the dependent variable, y? A table with Apple Juice (x), Grape Juice (y) and Grape Juice/Apple Juice (y/x). The first row has x as 5 and y as 8. The second row has x as 10 and y as 16. In each row, the ratio of Grape Juice to Apple Juice is a blank to be filled. The constant of proportionality is . An equation that represents this proportional relationship is =

Answer/Step-by-step explanation:

The equation that relates the proportional quantities would take the following form ---› [tex] y = kx [/tex], where,

y = amount of Grape juice (dependent variable)

x = amount of Apple juice (independent variable)

k = constant of proportionality (y/x)

✔️Using any of the given pair, say, (5, 8),

Constant of proportionality = [tex] k = \frac{y}{x} = \frac{8}{5} = 1.6 [/tex]

Substitute k = 1.6 in [tex] y = kx [/tex].

An equation that represents the proportional relationship would be:

[tex] y = 1.6x [/tex]

Or

[tex] y = \frac{8}{5}x [/tex]

How the equation would change if:

y = amount of Apple juice (dependent variable)

x = amount of Grape juice (independent variable)

The constant of proportionality would change, that is using a pair, say, (8, 5),

[tex] k = \frac{y}{x} = \frac{5}{8} = 0.625 [/tex]

Substitute k = 0.625 in [tex] y = kx [/tex].

The equation would now be:

[tex] y = 0.625x [/tex].

Or

[tex] y = \frac{5}{8}x [/tex]

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