Question

The table shows the ratio of nuts to raisins in different snack mixes.


Snack Mix Ratios
Nuts (x)
Raisins (y)
6
9
12
18
18
27
24
36

Which graph shows these equivalent ratios?
mc006-1.jpg
mc006-2.jpg
mc006-3.jpg
mc006-4.jpg

Answer 1

To find the equivalent ratios of nuts to raisins, we can simplify the given ratios. The ratio of nuts (x) to raisins (y) in the snack mixes is as follows:

- For \( (6, 9) \): Simplifying gives \( \frac{6}{9} = \frac{2}{3} \)
- For \( (12, 18) \): Simplifying gives \( \frac{12}{18} = \frac{2}{3} \)
- For \( (18, 27) \): Simplifying gives \( \frac{18}{27} = \frac{2}{3} \)
- For \( (24, 36) \): Simplifying gives \( \frac{24}{36} = \frac{2}{3} \)

All the ratios simplify to \( \frac{2}{3} \).

To determine which graph shows these equivalent ratios, look for a linear graph that has a slope representing the ratio of \( \frac{Nuts}{Raisins} \) = \( \frac{2}{3} \). This can be represented as \( y = \frac{3}{2}x \) or equivalently, \( x = \frac{2}{3}y \).

Please check the offered graphs for the one that has this slope or represents the points \( (6, 9), (12, 18), (18, 27), (24, 36) \) as a straight line, indicating equivalent ratios.

If the graphs are not available to view in this session, please let me know how I can help you further!