Answer :
Sure, let's solve the equation [tex]\( x - 2y = 8 \)[/tex] to convert it to the slope-intercept form, which is [tex]\( y = mx + b \)[/tex]. Here's a step-by-step explanation:
1. Start with the given equation:
[tex]\[ x - 2y = 8 \][/tex]
2. Isolate the [tex]\( y \)[/tex] term on one side of the equation. To do this, move the [tex]\( x \)[/tex] term to the right side by subtracting [tex]\( x \)[/tex] from both sides:
[tex]\[ -2y = -x + 8 \][/tex]
3. Next, solve for [tex]\( y \)[/tex] by dividing all terms by -2:
[tex]\[ y = \frac{-x + 8}{-2} \][/tex]
4. Simplify the equation:
[tex]\[
y = \frac{-x}{-2} + \frac{8}{-2}
\][/tex]
[tex]\[
y = \frac{1}{2}x - 4
\][/tex]
5. So, the slope-intercept form of the equation is:
[tex]\[
y = \frac{1}{2} x - 4
\][/tex]
Therefore, the equation [tex]\( y = \frac{1}{2} x - 4 \)[/tex] corresponds to the answer choice:
[tex]\[ y = \frac{1}{2} x - 4 \][/tex]
Hence, the correct answer is:
[tex]\[ y = \frac{1}{2} x - 4 \][/tex]
Which corresponds to the last choice in the given options.
1. Start with the given equation:
[tex]\[ x - 2y = 8 \][/tex]
2. Isolate the [tex]\( y \)[/tex] term on one side of the equation. To do this, move the [tex]\( x \)[/tex] term to the right side by subtracting [tex]\( x \)[/tex] from both sides:
[tex]\[ -2y = -x + 8 \][/tex]
3. Next, solve for [tex]\( y \)[/tex] by dividing all terms by -2:
[tex]\[ y = \frac{-x + 8}{-2} \][/tex]
4. Simplify the equation:
[tex]\[
y = \frac{-x}{-2} + \frac{8}{-2}
\][/tex]
[tex]\[
y = \frac{1}{2}x - 4
\][/tex]
5. So, the slope-intercept form of the equation is:
[tex]\[
y = \frac{1}{2} x - 4
\][/tex]
Therefore, the equation [tex]\( y = \frac{1}{2} x - 4 \)[/tex] corresponds to the answer choice:
[tex]\[ y = \frac{1}{2} x - 4 \][/tex]
Hence, the correct answer is:
[tex]\[ y = \frac{1}{2} x - 4 \][/tex]
Which corresponds to the last choice in the given options.
