Determine which type of rule is represented in the table. What are the missing values?(1 point)

Question

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:

$$\text{Misplaced hline}$$

Missing values:

• For $x=30$, $y=150$
• For $x=35$, $y=175$

The rule indicated by the table is $y=5x$.