Question

Determine which type of rule is represented in the table. What are the missing values?(1 point)
x
y
25 125
30
35
40 200

Answer 1

To determine the type of rule represented in the table, let's first analyze the given pairs of values for \(x\) and \(y\):

- When \(x = 25\), \(y = 125\).
- When \(x = 40\), \(y = 200\).

Let's look for a possible relationship between \(x\) and \(y\). A common type of relationship is a linear or polynomial one. Let's explore whether there's a multiplication or division relationship between the values.

Calculating the ratio of \(y\) to \(x\) for the known values:

1. For \(x = 25\):
\[
\frac{y}{x} = \frac{125}{25} = 5
\]

2. For \(x = 40\):
\[
\frac{y}{x} = \frac{200}{40} = 5
\]

The ratio of \(y\) to \(x\) is the same (5) for both values. This suggests that there is a linear relationship given by the equation:

\[
y = 5x
\]

Now, let's use this rule to find the missing values for \(y\) when \(x = 30\) and \(x = 35\):

1. For \(x = 30\):
\[
y = 5 \times 30 = 150
\]

2. For \(x = 35\):
\[
y = 5 \times 35 = 175
\]

So, the completed table with the missing values is:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
25 & 125 \\
30 & 150 \\
35 & 175 \\
40 & 200 \\
\hline
\end{array}
\]

**Missing values:**
- For \(x = 30\), \(y = 150\)
- For \(x = 35\), \(y = 175\)

The rule indicated by the table is \(y = 5x\).