Given that 2x + y + 4 = 0, answer the following:   a) y - intercept = ?   b) slope = ?   c) x - intercept = ?

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 \( y = mx + b \).

Given that 2x + y + 4 = 0, answer the following: a) y-intercept = ? b) slope = ? c) x-intercept = ?

Discover how to find the slope, y-intercept, and x-intercept of the linear equation 2x + y + 4 = 0. This guide provides a clear, step-by-step solution, ideal for students in Grades 8-10 who are learning about linear equations and coordinate geometry.

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