Question

What equation represents the proportional relationship displayed in the table?

x 0 4 7 8
y 0 24 42 48
Enter your answer by filling in the box to complete the equation.

y =
x

Answer 1

To find the equation that represents the proportional relationship displayed in the table, we can first determine the constant of proportionality (k) by using any pair of (x, y) values from the table.

Using the pair \( (4, 24) \):

\[
k = \frac{y}{x} = \frac{24}{4} = 6
\]

Now, let's check this with another (x, y) pair, \( (7, 42) \):

\[
k = \frac{42}{7} = 6
\]

And another pair, \( (8, 48) \):

\[
k = \frac{48}{8} = 6
\]

Since all pairs give the same value for k, we confirm that the constant of proportionality is 6. Therefore, the equation that represents this proportional relationship is:

\[
y = 6x
\]

So, the completed equation is:

\[
y = 6x
\]