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?

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!