Answer :
To convert the equation [tex]\( x - 2y = 8 \)[/tex] into slope-intercept form, you need to perform the following steps:
1. Start with the standard form equation:
[tex]\[ x - 2y = 8 \][/tex]
2. Isolate the [tex]\( y \)[/tex]-term on one side of the equation by subtracting [tex]\( x \)[/tex] from both sides:
[tex]\[ -2y = -x + 8 \][/tex]
3. Divide every term by [tex]\(-2\)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{-x + 8}{-2} \][/tex]
4. Simplify the right side of the equation:
[tex]\[ y = \frac{-x}{-2} + \frac{8}{-2} \][/tex]
[tex]\[ y = \frac{1}{2}x - 4 \][/tex]
So, the equation [tex]\( y = \frac{1}{2}x - 4 \)[/tex] is in slope-intercept form, which is [tex]\( y = mx + b \)[/tex] where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Comparing this form with the given answer choices:
- [tex]\( y=\frac{1}{2} x+4 \)[/tex]
- [tex]\( y=-\frac{1}{2} x+4 \)[/tex]
- [tex]\( y=-\frac{1}{2} x-4 \)[/tex]
- [tex]\( y=\frac{1}{2} x-4 \)[/tex]
The correct answer is:
[tex]\[ y = \frac{1}{2} x - 4 \][/tex]
Therefore, the answer is:
[tex]\( \boxed{y=\frac{1}{2} x-4} \)[/tex]
1. Start with the standard form equation:
[tex]\[ x - 2y = 8 \][/tex]
2. Isolate the [tex]\( y \)[/tex]-term on one side of the equation by subtracting [tex]\( x \)[/tex] from both sides:
[tex]\[ -2y = -x + 8 \][/tex]
3. Divide every term by [tex]\(-2\)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{-x + 8}{-2} \][/tex]
4. Simplify the right side of the equation:
[tex]\[ y = \frac{-x}{-2} + \frac{8}{-2} \][/tex]
[tex]\[ y = \frac{1}{2}x - 4 \][/tex]
So, the equation [tex]\( y = \frac{1}{2}x - 4 \)[/tex] is in slope-intercept form, which is [tex]\( y = mx + b \)[/tex] where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Comparing this form with the given answer choices:
- [tex]\( y=\frac{1}{2} x+4 \)[/tex]
- [tex]\( y=-\frac{1}{2} x+4 \)[/tex]
- [tex]\( y=-\frac{1}{2} x-4 \)[/tex]
- [tex]\( y=\frac{1}{2} x-4 \)[/tex]
The correct answer is:
[tex]\[ y = \frac{1}{2} x - 4 \][/tex]
Therefore, the answer is:
[tex]\( \boxed{y=\frac{1}{2} x-4} \)[/tex]
