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:
-
For \(x = 25\): \[ \frac{y}{x} = \frac{125}{25} = 5 \]
-
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 \(x = 35\):
-
For \(x = 30\): \[ y = 5 \times 30 = 150 \]
-
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 \(y = 5x\).
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