To find the slope and [tex]\( y \)[/tex]-intercept of the equation [tex]\( 2x - 4y = -4 \)[/tex], we will convert it to the slope-intercept form of a linear equation, which is [tex]\( y = mx + b \)[/tex]. In this form, [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept.
1. Start with the given equation:
[tex]\[
2x - 4y = -4
\][/tex]
2. Isolate the [tex]\( y \)[/tex]-term on one side of the equation:
Subtract [tex]\( 2x \)[/tex] from both sides of the equation:
[tex]\[
-4y = -2x - 4
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
Divide every term by [tex]\( -4 \)[/tex] to isolate [tex]\( y \)[/tex]:
[tex]\[
y = \frac{-2x}{-4} + \frac{-4}{-4}
\][/tex]
4. Simplify the fractions:
[tex]\[
y = \frac{1}{2}x + 1
\][/tex]
Now, we can easily identify the slope and the [tex]\( y \)[/tex]-intercept from the equation [tex]\( y = \frac{1}{2}x + 1 \)[/tex]:
- The slope ([tex]\( m \)[/tex]) is [tex]\( \frac{1}{2} \)[/tex].
- The [tex]\(y\)[/tex]-intercept is [tex]\( 1 \)[/tex] (which means the point [tex]\( (0, 1) \)[/tex]).
Therefore:
Slope [tex]\( (m) = 0.5 \)[/tex]
Y-intercept [tex]\( = 1 \)[/tex]
