To find the equation of line $B$ which passes through point $P$ and is parallel to line $A$, let's analyze the steps needed to solve this:

1. Identify the slope of line $A$: Since line $B$ is parallel to line $A$, it will have the same slope as line $A$. We can determine the slope by choosing two points on line $A$ from the graph and calculating the slope $m$ using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

2. Equation of line $A$: By identifying points along line $A$, we can find its slope. From the graph, let's choose two points on line $A$ to determine this slope.

3. Point $P$: Note the coordinates of point $P$ (let's call them $(x_1, y_1)$), which will serve as a reference point for line $B$.

4. Formulate the equation of line $B$: Using the point-slope form of a line $y - y_1 = m(x - x_1)$, substitute the slope $m$ (same as line $A$) and the coordinates of point $P$.

5. Convert to slope-intercept form $y = mx + c$: Simplify the equation to get it in the form $y = mx + c$.

Let’s go through these steps with the values from the graph:

1. Identify the coordinates of two points on line $A$ to find its slope.
2. Identify the coordinates of point $P$.
3. Substitute values into the point-slope form.

Once you try these steps, let me know if you want further assistance or if I should solve it with specific values from the graph.

Would you like a more detailed solution with specific values?

Here are 5 additional questions to expand your understanding:

1. How can you determine if two lines are parallel based on their slopes?
2. What happens to the equation of a line if it shifts vertically but remains parallel to its original?
3. How does changing the slope affect the steepness of the line?
4. Why is the point-slope form useful for finding the equation of a line through a given point?
5. How can you verify if a point lies on a specific line by using its equation?

Tip: When two lines are parallel, they always have the same slope but different $y$-intercepts (unless they are the same line).