The equation of the line is $y = 4x + 3$. The slope of the line is given by the coefficient of $x$, which is 4.

To find the angle $\theta$ between the line and the x-axis, we use the formula:

$\tan(\theta) = \text{slope of the line}$

In this case, the slope is 4, so:

$\tan(\theta) = 4$

Now, to find $\theta$, we take the arctangent (inverse tangent) of 4:

$\theta = \tan^{-1}(4)$

Let me calculate this value for you.

The angle between the line $y = 4x + 3$ and the x-axis is approximately $75.96^\circ$.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How would the angle change if the slope of the line was negative?
2. What is the angle between the line $y = -4x + 3$ and the x-axis?
3. How can you find the angle between two intersecting lines?
4. What is the relationship between the slope and angle in general?
5. How does the y-intercept affect the orientation of the line?

Tip: When a line has a positive slope, the angle between the line and the x-axis is always less than $90^\circ$, but greater than $0^\circ$.