To identify the missing equivalent ratios from the coordinate plane based on the data provided in the tables for Option A and Option B, we need to analyze the relationships given:
Option A:
The relationship between megabytes (x) and seconds (y) is as follows:
- For \( x = 7 \) (megabytes), \( y = 2 \) (seconds)
- For \( x = 14 \) (megabytes), \( y = 4 \) (seconds)
- The pattern suggests that for every increase of 7 megabytes, the time in seconds increases by 2 seconds.
The relationship can be formulated as: \[ \frac{y}{x} = \frac{2}{7} \] This means that for every 7 megabytes, there are 2 seconds of time taken.
So, we can find the equivalent ratios:
- For \( 21 \) megabytes: \[ y = \frac{2}{7} \times 21 = 6 \text{ seconds (already provided)} \]
Option B:
The relationship for Option B is:
- For \( x = 8 \) (megabytes), \( y = 3 \) (seconds)
- For \( x = 16 \) (megabytes), \( y = 6 \) (seconds)
The pattern here also suggests that for every 8 megabytes, the seconds increase by 3 seconds.
The relationship can be formulated as: \[ \frac{y}{x} = \frac{3}{8} \]
Using this, we can find equivalent ratios:
- For \( 24 \) megabytes: \[ y = \frac{3}{8} \times 24 = 9 \text{ seconds} \]
Summary of Equivalent Ratios:
From the analysis, we can conclude the equivalent ratios based on the patterns:
- From Option A:
- (21, 6) is already present.
- From Option B:
- (16, 6) is already present, and the next ratio would be (24, 9).
Thus, based on the coordinate plane, the missing equivalent ratios that you can report are:
- For Option A: (21, 6)
- For Option B: (24, 9)
These values (if checked against the axis) indicate all plotted points accurately reflect the mentioned relationships concerning both data sizes and respective time durations.