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A linear relationship is shown in the table.
\begin{tabular}{|c|c|c|c|c|}
\hline Time (hours) & 2 & 4 & 6 & 8 \\
\hline Distance (miles) & 8 & 16 & 24 & 32 \\
\hline
\end{tabular}

Is the linear relationship also proportional? Explain.

A. Yes, the constant of proportionality is 4.
B. Yes, there is no constant of proportionality.
C. No, the constant of proportionality is 4.
D. No, there is no constant of proportionality.



Answer :

GinnyAnswer
To determine whether the relationship between time and distance in the table is proportional, we should follow these steps:

1. Calculate the ratio of distance to time for each pair of values.
2. Check if these ratios are the same across all pairs.

Given data:
[tex]\[ \begin{array}{ccc} \hline \text{Time (hours)} & 2 & 4 & 6 & 8 \\ \hline \text{Distance (miles)} & 8 & 16 & 24 & 32 \\ \hline \end{array} \][/tex]

1. Calculate the ratios:

[tex]\[ \text{Ratio} = \frac{\text{Distance}}{\text{Time}} \][/tex]

- For 2 hours and 8 miles:
[tex]\[ \frac{8}{2} = 4 \][/tex]

- For 4 hours and 16 miles:
[tex]\[ \frac{16}{4} = 4 \][/tex]

- For 6 hours and 24 miles:
[tex]\[ \frac{24}{6} = 4 \][/tex]

- For 8 hours and 32 miles:
[tex]\[ \frac{32}{8} = 4 \][/tex]

2. Check the ratios:
All the calculated ratios are 4.

Since the ratio \(\frac{\text{Distance}}{\text{Time}}\) is constant (4) for all pairs in the table, the relationship between time and distance is indeed proportional. This constant ratio is known as the constant of proportionality.

Therefore, the answer is:
Yes, the constant of proportionality is 4.

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