Question

Use the tables and image to answer the question.

This table shows the relationship between the data size in megabytes (in multiples of 7) and the corresponding time duration in seconds.
Option A
x
(megabytes) y
(seconds)
7 2
14 4
21 6
This table shows the relationship between the data size in megabytes (in multiples of 8) and the corresponding time duration in seconds.
Option B
x
(megabytes) y
(seconds)
8 3
16 6


A graph with the x-axis representing megabytes ranging from 0 to 22 in increments of 1 and the y-axis representing seconds ranging from 0 to 7 in increments of 1 shows three plotted points, 2 for option A and 1 for option B. Option A has the following points: left parenthesis 7 comma 2 right parenthesis and left parenthesis 14 comma 4 right parenthesis. Option B has the following point: left parenthesis 8 comma 3 right parenthesis.

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

(2 points)

1 answer

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.