Question

1. 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? explain. (example 4) toothbrush b number of rotations time (s)

Explanation:

Step1: Find the unit rate for toothbrush B

The graph passes through the point \((1,75)\) and \((2,150)\). The unit rate (slope) \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(1,75)\) and \((x_2,y_2)=(2,150)\), \(m=\frac{150 - 75}{2 - 1}=75\) rotations per second.

Step2: Compare the unit rates

For toothbrush A, the equation is \(y = 78x\), so the unit rate is \(78\) rotations per second. For toothbrush B, the unit rate is \(75\) rotations per second.

Answer:

Toothbrush A is faster. Because the unit rate (number of rotations per second) of toothbrush A is \(78\) (from \(y = 78x\)) and the unit rate of toothbrush B is \(75\) (calculated from the graph's slope). Since \(78>75\), toothbrush A has more rotations per second.