The table shows the values of $x$ and $y$, and the question asks which type of relationship is represented.

Analyzing the Table

1. Differences in $y$: When $x$ increases by 1, $y$ increases by 2. This suggests a constant rate of change.

   • From $y = 19$ to $y = 21$: Difference = 2
   • From $y = 21$ to $y = 23$: Difference = 2
   • This constant increase indicates a linear relationship.

2. Linear Relationship: A linear relationship follows the formula: $y = mx + c$ where $m$ is the slope and $c$ is the y-intercept.

Equation for $y$:

From the table:

• When $x = 0$, $y = 19$, so $c = 19$.
• The slope $m = 2$ (rate of change of $y$).

Thus, the equation is: $y = 2x + 19$

Correct Answer:

Lineair verband (Linear Relationship).

Would you like a detailed explanation of the other options or further analysis?

Here are 5 related questions to expand on this topic:

1. How do you determine the type of relationship if the differences in $y$ are not constant?
2. Can you provide an example of a quadratic relationship in tabular form?
3. How would you identify a periodic relationship from a table of values?
4. What is the difference between linear and directly proportional relationships?
5. How do you derive the formula for $y$ from a table like this?

Tip: Always calculate differences in $y$ when identifying the relationship in a table.