To find the slope and the [tex]$y$[/tex]-intercept of the line given by the equation [tex]\( 4x + 2y = -2 \)[/tex], we need to rewrite the equation in the slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the [tex]$y$[/tex]-intercept.
### Step-by-Step Solution
1. Starting Equation:
[tex]\[
4x + 2y = -2
\][/tex]
2. Isolate the [tex]\( y \)[/tex]-term:
To do this, we first move the [tex]\( 4x \)[/tex] term to the other side of the equation by subtracting [tex]\( 4x \)[/tex] from both sides:
[tex]\[
2y = -4x - 2
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
Next, divide every term in the equation by 2 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = -2x - 1
\][/tex]
Now, the equation is in the slope-intercept form [tex]\( y = mx + b \)[/tex].
4. Identify the Slope ([tex]\( m \)[/tex]):
The coefficient of [tex]\( x \)[/tex] in the equation [tex]\( y = -2x - 1 \)[/tex] is the slope. Thus,
[tex]\[
\text{slope} = -2
\][/tex]
5. Identify the [tex]\( y \)[/tex]-Intercept ([tex]\( b \)[/tex]):
The constant term in the equation [tex]\( y = -2x - 1 \)[/tex] is the [tex]\( y \)[/tex]-intercept. Thus,
[tex]\[
y\text{-intercept} = -1
\][/tex]
### Final Answers:
- Slope: [tex]\(-2\)[/tex]
- [tex]\( y \)[/tex]-Intercept: [tex]\(-1\)[/tex]
These are the simplest forms of the slope and the [tex]\( y \)[/tex]-intercept for the given line equation.
