Use the tables and image to answer the question.

Question

Option A
x
(lemonade mix) y
(cups of water)
5 4
10 8
15 12
20 16
25 20
Option B
x
(lemonade mix) y
(cups of water)
6 5
12 10
18 15
24 20
A graph with the x-axis representing scoops of lemonade mix ranging from 0 to 30 in increments of 3 and the y-axis representing cups of water ranging from 0 to 20 in increments of 2 shows seven plotted points, 4 for option A and 3 for option B. Option A has the following points: left parenthesis 5 comma 4 right parenthesis; left parenthesis 10 comma 8 right parenthesis; left parenthesis 15 comma 12 right parenthesis; and left parenthesis 20 comma 16 right parenthesis. Option B has the following points: left parenthesis 6 comma 5 right parenthesis; left parenthesis 12 comma 10 right parenthesis; and left parenthesis 18 comma 15 right parenthesis.

Based on the tables and coordinate plane, identify the missing equivalent ratios from the coordinate plane.

(1 point)
(
)
; (
)

Answer 1

To find the missing equivalent ratios, we can analyze the ratio of lemonade mix (x) to cups of water (y) for both options.

Option A Ratios:

The ratios from Option A:

• \( \frac{5}{4} \)
• \( \frac{10}{8} \) which simplifies to \( \frac{5}{4} \)
• \( \frac{15}{12} \) which simplifies to \( \frac{5}{4} \)
• \( \frac{20}{16} \) which simplifies to \( \frac{5}{4} \)

This shows that all the ratios for Option A simplify to \( \frac{5}{4} \).

Option B Ratios:

The ratios from Option B:

• \( \frac{6}{5} \)
• \( \frac{12}{10} \) which simplifies to \( \frac{6}{5} \)
• \( \frac{18}{15} \) which simplifies to \( \frac{6}{5} \)

This shows that all the ratios for Option B simplify to \( \frac{6}{5} \).

Finding Missing Equivalent Ratios:

In the graph, we need to identify the equivalent ratios for the points corresponding to Options A and B.

For Option A:

• The point \( (25, 20) \) corresponds to the ratio \( \frac{25}{20} \) which simplifies to \( \frac{5}{4} \).

For Option B:

• The next ratio could be derived, for example, let's identify \( (30, 25) \), which corresponds to the ratio \( \frac{30}{25} \) which simplifies to \( \frac{6}{5} \).

Conclusion:

The missing equivalent ratios from the coordinate plane would be:

• For Option A: \( (25, 20) \)
• For Option B: \( (30, 25) \)

Answer: \( (25, 20); (30, 25) \)