https://file.aiquickdraw.com/mathbot/file/1726191197760ahef1xn0.jpg

https://file.aiquickdraw.com/mathbot/file/1726191197761o4pw7diw.jpg

Let's break down the problem based on the images you've provided:

### Part (a) - Finding the formula of the blue solid line:
The red dashed line has the equation:
\[
y = 4x + 3
\]
Since the blue solid line is parallel to the red dashed line, both lines have the same slope. Therefore, the slope of the blue line is also \( m = 4 \). The equation of the blue line will be in the form:
\[
y = 4x + b
\]
To find \( b \), we need a point on the blue line. From the graph, the blue line appears to cross the y-axis at \( y = -4 \). Therefore, the y-intercept \( b \) is \( -4 \).

Thus, the equation of the blue line is:
\[
y = 4x - 4
\]

### Part (b) - Finding the coordinates of point \( P \):
Point \( P \) lies on the blue line. From the graph, \( P \) appears to be on the positive x-axis at some point. Looking closely, it seems to be near \( x = 2 \).

To find the exact coordinates of point \( P \), substitute \( x = 2 \) into the equation of the blue line:
\[
y = 4(2) - 4 = 8 - 4 = 4
\]

Therefore, the coordinates of point \( P \) are \( (2, 4) \).

### Final answers:
1. The equation of the blue solid line is \( y = 4x - 4 \).
2. The coordinates of point \( P \) are \( (2, 4) \).

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Would you like more details on any part of the solution, or have additional questions?

### Related Questions:
1. How do you determine if two lines are parallel or perpendicular based on their equations?
2. How would the equation change if the blue line were perpendicular to the red line instead of parallel?
3. Can you find the equation of a line if you're given two points on it?
4. What happens if you translate the blue line vertically? How would the equation change?
5. How would you solve for the point of intersection if the lines were not parallel?

### Tip:
Parallel lines always have the same slope, but different y-intercepts, which is the key to solving these types of problems.

The red dashed line y = 4x + 3 and the blue solid line are parallel. (a) Find the formula of the blue solid line. (b) Find the coordinates of point P.

This problem focuses on determining the equation of a blue solid line parallel to a red dashed line y = 4x + 3, as well as finding the coordinates of point P on the blue line. It covers key concepts like linear equations, slope-intercept form, and parallel lines, suitable for Grades 8-10.

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