https://file.aiquickdraw.com/mathbot/file/17301173875554z7ptjsb.jpg

Let's analyze this problem.

### Given Information:
1. **Toothbrush A** is described by the equation:
   \[
   y = 78x
   \]
   where \( y \) represents the number of rotations after \( x \) seconds. This implies that **Toothbrush A** has a constant rotation rate of **78 rotations per second**.

2. **Toothbrush B** is represented by a graph showing the number of rotations over time.

### Analyzing Toothbrush B’s Rate:
Looking at the graph for Toothbrush B:
- At \( x = 1 \) second, the number of rotations \( y \) is about 50.
- At \( x = 2 \) seconds, \( y \) is around 100 rotations.

From these two points, we can calculate the rate of Toothbrush B as:
\[
\text{Rate} = \frac{\text{Change in rotations}}{\text{Change in time}} = \frac{100 - 50}{2 - 1} = 50 \text{ rotations per second}
\]

### Comparing Rates:
- **Toothbrush A** rotates at 78 rotations per second.
- **Toothbrush B** rotates at 50 rotations per second.

Since 78 > 50, **Toothbrush A** has a higher rate.

### Correct Answer:
The best answer is:
- **Option A:** "Toothbrush A, because its unit rate is greater by 3 rotations per second."

The equation y = 78x represents the number of rotations per second for electric toothbrush A. The graph shows the number of rotations for electric toothbrush B. Which toothbrush is faster? Select the best answer.

Learn how to compare the speed of two electric toothbrushes using linear equations and unit rate analysis. Given the equation y = 78x for toothbrush A and a graph for toothbrush B, determine which toothbrush has a higher rotation rate. Suitable for Grade 8 students.

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