Let's solve the problem based on the provided image.

Given:

1. The equation of the line is $y = ax + b$, where $a$ and $b$ are constants.
2. The line has a $y$-intercept of $(0, 3)$. This implies $b = 3$.
3. The line is parallel to the line $y = 2x$. Parallel lines have the same slope, so $a = 2$.
4. We need to find the value of $a + b$.

Solution:

• From point 2, $b = 3$.
• From point 3, $a = 2$.
• Therefore, $a + b = 2 + 3 = 5$.

Final Answer:

The value of $a + b$ is 5.

Would you like a detailed breakdown or have additional questions?
Here are five related questions to explore:

1. How do you find the slope of a line from its equation?
2. Why do parallel lines have the same slope?
3. What happens to the equation of a line if its $y$-intercept changes?
4. How do you determine if two lines are perpendicular?
5. How do you find the equation of a line passing through two points?

Tip: When solving geometry problems involving parallel lines, always compare their slopes first.