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We are given the equation of a line: 
\[
y + 8 = -4(x - 4.5)
\]
Our goal is to find the **y-intercept** of the line, which occurs when \(x = 0\).

### Steps:
1. **Simplify the given equation**:
   Start by isolating \(y\) on the left side of the equation. 

\[
y = -4(x - 4.5) - 8
\]

2. **Expand** the right-hand side:
\[
y = -4(x - 4.5) - 8 = -4x + 18 - 8
\]
\[
y = -4x + 10
\]

3. **Identify the y-intercept**:
   The equation is now in slope-intercept form \(y = mx + b\), where \(b\) represents the y-intercept. Here, the y-intercept is \(b = 10\).

### Final Answer:
The y-intercept is **10**.

Would you like a more detailed explanation or have any other questions?

### Related Questions:
1. How do you find the slope from this equation?
2. What is the x-intercept of the same line?
3. Can you graph the line based on the equation?
4. How does the slope influence the steepness of the line?
5. What would happen to the y-intercept if the slope changed?

### Tip:
The y-intercept is always the value of \(y\) when \(x = 0\), so solving for \(y\) at \(x = 0\) gives you this important point.

What is the y-intercept of the line y + 8 = -4(x - 4.5)?

Learn how to find the y-intercept of the linear equation y + 8 = -4(x - 4.5) using the slope-intercept form. This problem is suitable for students in Grades 8-10 and covers key algebraic concepts such as linear equations and y-intercept calculations.

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