Question

Damian can make 3 free-throws in 10 seconds and 18 free throwsin 1 minute. What is the constant proportionality?

Answer 1

Consider x to be the number of seconds and y the number of free-throws.

Then, according to the question, the equation includes points (10,3) and (60,18).

Finding the equation of a line that goes through such two points,

$\begin{gathered} (10,3),(60,18) \\ \Rightarrow y-3=(\frac{18-3}{60-10})(x-10) \\ \Rightarrow y-3=0.3x-3 \\ \Rightarrow y=0.3x \end{gathered}$

Thus, the constant of proportionality is 0.3. 0.3 free-throws per second or 3.333... seconds per free-throw