Question

there are 1000 centimeters in 10 meters. what does the constant of proportionality of 100 mean? the constant of proportionality is 100. the constant of proportionality of 100 means that there are 100 centimeters for every meter 100 meters for every centimeter

Explanation:

Step1: Recall proportion concept

In a proportional relationship between meters and centimeters, if $y$ is the number of centimeters and $x$ is the number of meters, the equation is $y = kx$, where $k$ is the constant of proportionality.

Step2: Analyze given data

We know that when $x = 10$ meters, $y=1000$ centimeters. Substituting into $y = kx$, we get $1000=k\times10$. Solving for $k$, we divide both sides by 10: $k=\frac{1000}{10}=100$. This means for every 1 - unit increase in the number of meters ($x$), the number of centimeters ($y$) increases by 100.

Answer:

100 centimeters for every meter