To find the rule in the form $y = mx + b$, let's determine the slope $m$ and y-intercept $b$ for this relationship.

1. Calculate the slope (m): The slope $m$ is given by the formula: $m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$

   Using the points $(0, 5)$ and $(3, 11)$: $m = \frac{11 - 5}{3 - 0} = \frac{6}{3} = 2$

   So, $m = 2$.

2. Determine the y-intercept (b): Substitute $m = 2$ and the point $(0, 5)$ into the equation $y = mx + b$: $5 = 2 \cdot 0 + b \Rightarrow b = 5$

   Therefore, the equation is: $y = 2x + 5$

Final Answer: $y = 2x + 5$

Would you like further explanation on any step, or do you have any other questions?

Here are five related questions to deepen understanding:

1. How do you find the equation of a line if given two points?
2. What does the slope represent in the context of a linear equation?
3. How would the equation change if the y-intercept was different?
4. How can you verify that a point lies on the line described by a given equation?
5. What is the difference between positive and negative slopes in linear equations?

Tip: To check your equation, substitute different $x$ values from the table and verify that they produce the corresponding $y$ values.