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The given linear equation is \( 4x + y + 2 = 0 \). 

To determine the **x-intercept** and **y-intercept**, let's proceed step by step:

### Part 1: Find the \(x\)-intercept
The \(x\)-intercept occurs when \(y = 0\). Substituting \(y = 0\) into the equation:
\[
4x + 0 + 2 = 0 \quad \Rightarrow \quad 4x + 2 = 0
\]
Solve for \(x\):
\[
4x = -2 \quad \Rightarrow \quad x = \frac{-2}{4} = -\frac{1}{2}
\]
Thus, the \(x\)-intercept is \((- \frac{1}{2}, 0)\), so \(a = -\frac{1}{2}\).

### Part 2: Find the \(y\)-intercept
The \(y\)-intercept occurs when \(x = 0\). Substituting \(x = 0\) into the equation:
\[
4(0) + y + 2 = 0 \quad \Rightarrow \quad y + 2 = 0
\]
Solve for \(y\):
\[
y = -2
\]
Thus, the \(y\)-intercept is \((0, -2)\), so \(b = -2\).

### Final Answers:
- \(a = -\frac{1}{2}\)
- \(b = -2\)

Would you like further details or have any questions?

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Here are 5 related questions to further your understanding:

1. How do you graph a line using only the intercepts?
2. What is the slope of the line \( 4x + y + 2 = 0 \)?
3. Can you express the equation \( 4x + y + 2 = 0 \) in slope-intercept form?
4. How would you solve for intercepts if the equation included fractions?
5. How do you determine if two lines are parallel using their equations?

**Tip:** Always check your intercepts by substituting them back into the original equation to verify their correctness!

Determine the x and y intercepts for the given linear equation: 4x + y + 2 = 0.

Learn how to determine the x and y intercepts for the linear equation 4x + y + 2 = 0. This problem covers key concepts in linear equations, intercepts, and graphing. Suitable for students in Grades 9-10.

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