To find the point of intersection (p.o.i) of the line \( y = 4x + 1 \), you need to determine where this line intersects with another curve or line. However, since only one equation is provided, it seems like you may be looking for additional context, such as its intersection with an axis or another equation.

If you're referring to the intersection with the **x-axis** or **y-axis**, here's the method:

1. **Intersection with the x-axis**: Set \( y = 0 \) because on the x-axis, \( y = 0 \).
   
   \[
   0 = 4x + 1
   \]
   Solve for \( x \):
   \[
   4x = -1
   \]
   \[
   x = -\frac{1}{4}
   \]
   So the intersection with the x-axis is at \( \left( -\frac{1}{4}, 0 \right) \).

2. **Intersection with the y-axis**: Set \( x = 0 \) because on the y-axis, \( x = 0 \).
   
   \[
   y = 4(0) + 1 = 1
   \]
   So the intersection with the y-axis is at \( (0, 1) \).

If this is not what you meant by the "point of intersection," let me know. Otherwise, here are more relative questions you might be interested in:

1. How do you find the point of intersection between two linear equations?
2. Can a line intersect a quadratic equation at more than one point?
3. What is the method to find the intersection of two curves geometrically?
4. How can we apply matrices to solve systems of equations for intersections?
5. How does the slope of a line affect its intersections with the axes?

**Tip:** For intersections of two lines, you set the equations equal to each other and solve for \(x\) and \(y\).

Learn how to find the points of intersection of the linear equation y = 4x + 1 with the x-axis and y-axis. This problem covers key algebraic concepts like solving for x and y in linear equations, ideal for students in Grades 8-10.

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