Question

Find the constant of proportionality (unit rate) for the table and write the equation.
X Y
1 5 3 15 4 20 6 30

Answer 1

To find the constant of proportionality (unit rate) from the table, we can analyze the values of \(Y\) in relation to \(X\). The constant of proportionality can be determined by dividing each \(Y\) value by its corresponding \(X\) value.

Here's how to compute it for each pair:

1. For \(X = 1\), \(Y = 5\):
\[
\frac{Y}{X} = \frac{5}{1} = 5
\]

2. For \(X = 3\), \(Y = 15\):
\[
\frac{Y}{X} = \frac{15}{3} = 5
\]

3. For \(X = 4\), \(Y = 20\):
\[
\frac{Y}{X} = \frac{20}{4} = 5
\]

4. For \(X = 6\), \(Y = 30\):
\[
\frac{Y}{X} = \frac{30}{6} = 5
\]

In each case, the constant of proportionality (unit rate) is \(5\).

Now, we can write the equation that represents the relationship between \(X\) and \(Y\). Since \(Y\) is directly proportional to \(X\), we can express this relationship as:

\[
Y = 5X
\]

This equation indicates that for every unit increase in \(X\), \(Y\) increases by \(5\).