Question

5) Decide whether the table represents a proportional relationship. Explain how you know and show your work. distance it can be seen (miles) height of a lighthouse (feet) 6 20 9 45 11 70 13 95

Answer 1

From the values given in the table, we can see that the ratio of the height of the light house to the distance it can be seen is not contant.

$\begin{gathered} \frac{20}{6}=\frac{10}{3} \\ \frac{45}{9}=5 \\ \frac{70}{11},\frac{95}{13} \end{gathered}$

Since the ratio is not constant, they are not in direct proportion relation.

Also, their product is not fixed.

$\begin{gathered} 20\times6=120 \\ 45\times9=395 \\ 70\times11=770 \\ 95\times13=1235 \end{gathered}$

Since their product is not constnat, they are not in inverse proportional relation ship.

Therefore, we can say that the table doesn't represent a proportional relationship.