Question

1. tommy was jumping down his sidewalk. he made two jumps every 3 seconds. is the relationship between time and his number of jumps proportional? yes / no explain:

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship between two quantities \(x\) (time) and \(y\) (number of jumps) means \(y = kx\), where \(k\) is a constant (the unit rate). The ratio \(\frac{y}{x}\) should be constant.

Step2: Calculate the Rate

Tommy makes 2 jumps every 3 seconds. The rate of jumps per second is \(\frac{2}{3}\) jumps per second. For any time \(t\) (in seconds), the number of jumps \(j\) would be \(j=\frac{2}{3}t\). The ratio \(\frac{j}{t}=\frac{2}{3}\), which is constant. So the relationship is proportional.

Answer:

Yes. Because the number of jumps (\(j\)) and time (\(t\)) follow \(j = \frac{2}{3}t\), where the ratio \(\frac{j}{t}=\frac{2}{3}\) (constant), satisfying proportional relationship.