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The question asks for the equation of a line parallel to Line A and passing through point P. To solve this, follow these steps:

1. **Determine the slope (m)** of Line A:
   Since the new line must be parallel to Line A, both lines will have the same slope. To find the slope of Line A, we use the formula for the slope between two points on the line: 
   
   \[
   m = \frac{{y_2 - y_1}}{{x_2 - x_1}}
   \]
   
   Looking at the graph, Line A passes through points \((0, 3)\) and \((6, 6)\).
   
   So:
   \[
   m = \frac{6 - 3}{6 - 0} = \frac{3}{6} = \frac{1}{2}
   \]
   The slope of Line A, and therefore the new line, is \( m = \frac{1}{2} \).

2. **Use the point-slope form of the equation**:
   Now, we use the point-slope form of the line equation, which is:
   
   \[
   y - y_1 = m(x - x_1)
   \]
   
   Point P has coordinates \((-6, 5)\), so substituting into the equation:
   
   \[
   y - 5 = \frac{1}{2}(x + 6)
   \]

3. **Simplify to the slope-intercept form (y = mx + c)**:
   Distribute the \(\frac{1}{2}\):
   
   \[
   y - 5 = \frac{1}{2}x + 3
   \]
   
   Now, add 5 to both sides:
   
   \[
   y = \frac{1}{2}x + 8
   \]

Thus, the equation of the line is:

\[
y = \frac{1}{2}x + 8
\]

This is in the required form \(y = mx + c\), where \(m = \frac{1}{2}\) and \(c = 8\).

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Do you want more details or have any questions? Here are some related questions:

1. How do you find the slope if two points are not obvious on a graph?
2. What happens to the equation if the line is perpendicular instead of parallel?
3. Can you explain how changing the slope affects the direction of the line?
4. How do you convert between different forms of linear equations (e.g., point-slope to slope-intercept)?
5. How would the equation change if point P was different?

**Tip**: When finding the slope between two points, make sure to keep the order of subtraction consistent to avoid errors.

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 problem involves calculating the slope, applying the point-slope form, and converting to slope-intercept form. Suitable for students in Grades 8-10.

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