Given the equation $2x + y + 4 = 0$, let's first rewrite the equation in the standard slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. Rearrange the equation:

$y = -2x - 4$

Now, let's answer each question based on this form.

a) y-intercept

The y-intercept is the value of $y$ when $x = 0$. From the equation $y = -2x - 4$, we see that the y-intercept $b$ is $-4$.

Answer: y-intercept = -4

b) Slope

The slope of the line is the coefficient of $x$ in the equation. From $y = -2x - 4$, the slope $m$ is $-2$.

Answer: Slope = -2

c) x-intercept

The x-intercept is the value of $x$ when $y = 0$. Setting $y = 0$ in the equation:

$0 = -2x - 4$

Solve for $x$:

$2x = -4$

$x = -2$

Answer: x-intercept = -2

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Would you like more details or have any questions? Here are some related questions to consider:

1. How would the graph of this line look?
2. If the slope were positive, how would the graph change?
3. Can you derive the slope and intercepts of a line from its general form $Ax + By + C = 0$?
4. What is the significance of the slope in real-world problems?
5. How can you find the intercepts from an equation like $3x - 5y + 7 = 0$?

Tip: To quickly identify the slope and y-intercept, always try to express the equation in the form $y = mx + b$.