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We are tasked with finding the equation of a line that passes through the point \((-3, 4)\) and is parallel to the line given by the equation \(x - y = 9\).

### Step-by-step Solution:

1. **Find the slope of the given line**:
   The equation of the given line is \(x - y = 9\). Let's rewrite it in slope-intercept form \(y = mx + b\), where \(m\) is the slope.

   \[
   x - y = 9
   \]
   Solving for \(y\), we get:
   \[
   y = x - 9
   \]

   From this, we see that the slope \(m\) of the line is 1.

2. **Find the slope of the parallel line**:
   Since the lines are parallel, they have the same slope. Therefore, the slope of the line we are looking for is also \(m = 1\).

3. **Use the point-slope form**:
   The point-slope form of a line is given by:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \((x_1, y_1)\) is the point through which the line passes, and \(m\) is the slope.

   Substituting \(m = 1\) and the point \((-3, 4)\), we get:
   \[
   y - 4 = 1(x + 3)
   \]
   Simplifying this equation:
   \[
   y - 4 = x + 3
   \]
   \[
   y = x + 7
   \]

So, the equation of the line that passes through \((-3, 4)\) and is parallel to \(x - y = 9\) is:
\[
y = x + 7
\]

Would you like more details on this solution or have any questions?

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Here are 5 related questions to expand on this topic:

1. How do you find the equation of a line perpendicular to another line?
2. What is the slope-intercept form of a line, and why is it useful?
3. Can you find the equation of a line that passes through two points?
4. How does the point-slope form of a line differ from the slope-intercept form?
5. What is the general form of a linear equation, and how do you convert between forms?

**Tip:** When finding equations of parallel lines, remember that they always have identical slopes!

What is an equation of the line that passes through the point (-3, 4) and is parallel to the line x - y = 9?

Learn how to find the equation of a line that passes through the point (-3, 4) and is parallel to the line x - y = 9. This solution explains key algebraic concepts, such as the slope-intercept form and the point-slope form, and how to apply them. Suitable for students in Grades 8-10.

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