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The problem asks to write the equation of a line that is parallel to \( y = -4x + 7 \) and passes through the point \( C(4, 5) \).

### Steps to solve:
1. **Identify the slope of the given line**:
   The slope of the line \( y = -4x + 7 \) is \( -4 \) (since the equation is in slope-intercept form \( y = mx + b \), where \( m \) is the slope).

2. **Use the point-slope form**:
   To find the equation of a line parallel to this one, we need to use the same slope (\( -4 \)) and the point \( C(4, 5) \). The point-slope form of a line is:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) \) is the point and \( m \) is the slope.

   Substituting \( m = -4 \), \( x_1 = 4 \), and \( y_1 = 5 \):
   \[
   y - 5 = -4(x - 4)
   \]
   
3. **Simplify the equation**:
   Expanding the right-hand side:
   \[
   y - 5 = -4x + 16
   \]
   Add 5 to both sides:
   \[
   y = -4x + 21
   \]

### Final Answer:
The equation of the line parallel to \( y = -4x + 7 \) and passing through the point \( C(4, 5) \) is:
\[
y = -4x + 21
\]

Would you like further details on any of these steps or have additional questions?

Here are some related questions:
1. What is the general form of the equation of a line?
2. How do you find the equation of a line perpendicular to a given line?
3. What is the significance of the slope in the equation of a line?
4. How would the equation change if the line passed through a different point?
5. How can we verify that two lines are parallel?

**Tip**: To quickly identify the slope of a line from an equation in slope-intercept form, simply look at the coefficient of \(x\).

Write an equation for the line parallel to the given line that contains point C(4, 5); y = -4x + 7.

Learn how to find the equation of a line parallel to y = -4x + 7 that passes through the point C(4,5). This problem covers key algebraic concepts such as parallel lines and the point-slope form of a linear equation. Suitable for students in Grades 8-10.

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