Question

The variables y and x have a proportional relationship, and y = 12 when x = 5.

What is the value of y when x = 8?

Enter your answer as a decimal in the box.

y =

Answer 1

In a proportional relationship, the relationship between \(y\) and \(x\) can be described by the equation:

\[
y = kx
\]

where \(k\) is the constant of proportionality.

From the information given, when \(y = 12\), \(x = 5\). We can find \(k\) as follows:

\[
12 = k \cdot 5
\]

To solve for \(k\):

\[
k = \frac{12}{5} = 2.4
\]

Now, we have the equation that describes the relationship between \(y\) and \(x\):

\[
y = 2.4x
\]

Now, we want to find the value of \(y\) when \(x = 8\). Substituting \(x = 8\) into the equation:

\[
y = 2.4 \cdot 8
\]

Calculating this gives:

\[
y = 19.2
\]

Thus, the value of \(y\) when \(x = 8\) is

\[
\boxed{19.2}
\]