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To solve this problem, we need to determine the equation of a line that is parallel to Line \( A \) and passes through point \( P \).

### Step 1: Determine the Slope of Line \( A \)

1. Identify two points on Line \( A \) from the graph. Let's choose:
   - Point \( (0, -2) \)
   - Point \( (2, 1) \)
   
2. Calculate the slope \( m \) of Line \( A \) using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting the values:
   \[
   m = \frac{1 - (-2)}{2 - 0} = \frac{3}{2}
   \]

So, the slope of Line \( A \) is \( \frac{3}{2} \).

### Step 2: Determine the Equation of the Line Passing Through Point \( P \) and Parallel to Line \( A \)

Since the line we want is parallel to Line \( A \), it will have the same slope, \( m = \frac{3}{2} \). 

We are given that this line passes through point \( P \) at \( (1, 3) \).

### Step 3: Use the Point-Slope Form to Find the Equation

The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
Substituting \( m = \frac{3}{2} \), \( x_1 = 1 \), and \( y_1 = 3 \):
\[
y - 3 = \frac{3}{2}(x - 1)
\]

### Step 4: Simplify the Equation

Expand and simplify to put it in the form \( y = mx + c \):
\[
y - 3 = \frac{3}{2}x - \frac{3}{2}
\]
\[
y = \frac{3}{2}x - \frac{3}{2} + 3
\]
\[
y = \frac{3}{2}x + \frac{3}{2}
\]

### Final Answer

The equation of the line parallel to Line \( A \) that passes through point \( P \) is:
\[
y = \frac{3}{2}x + \frac{3}{2}
\]

Would you like further details on any part of this solution? Here are some related questions to explore:

1. How can you find the equation of a line perpendicular to Line \( A \) passing through point \( P \)?
2. What is the y-intercept of the new line compared to Line \( A \)?
3. How would the equation change if point \( P \) were different?
4. How can you graphically verify the parallelism of two lines?
5. How do you determine if two lines are parallel from their equations alone?

**Tip:** Remember that parallel lines always have the same slope, so finding the slope is crucial in these types of problems.

The graph below shows line A and point P. Work out the equation of the straight line that is parallel to line A and passes through point P. Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.

Learn how to find the equation of a line parallel to a given line and passing through a specific point. This solution covers the concepts of slope, point-slope form, and parallel lines, suitable for students in Grades 8-10.

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