Question

gina has outgrown the bike she rode when she was small. so, for her twelfth birthday, her parents surprise her with a five - speed blaze rider 2000! gina has never had a bike with multiple speeds before, and she is eager to learn how it works. she starts by testing the middle speed. there is a proportional relationship between the number of times gina pedals, x, and the number of times the wheels rotate, y. \

$$\begin{tabular}{|c|c|} \\hline x (times gina pedals) & y (times the wheels rotate) \\\\ \\hline 4 & 8 \\\\ \\hline 7 & 14 \\\\ \\hline 9 & 18 \\\\ \\hline 10 & 20 \\\\ \\hline \\end{tabular}$$

what is the constant of proportionality? write your answer as a whole number or decimal. \boxed{} wheel rotations per time gina pedals

Explanation:

Step1: Recall the formula for proportional relationship

For a proportional relationship \( y = kx \), the constant of proportionality \( k \) is given by \( k=\frac{y}{x} \).

Step2: Calculate \( k \) using the first pair of values

Using \( x = 4 \) and \( y = 8 \), we substitute into the formula: \( k=\frac{8}{4}=2 \).
We can verify with other pairs: For \( x = 7 \), \( y = 14 \), \( k=\frac{14}{7}=2 \); for \( x = 9 \), \( y = 18 \), \( k=\frac{18}{9}=2 \); for \( x = 10 \), \( y = 20 \), \( k=\frac{20}{10}=2 \). All give \( k = 2 \).

Answer:

2