Question
Rewrite in slope-intercept form: \[ -2 x+2 y=16 \]
Ask by Wood Norris. in the United States
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The slope-intercept form of the equation is \( y = x + 8 \).
Solution
To rewrite the equation \(-2x + 2y = 16\) in slope-intercept form \((y = mx + b)\), follow these steps:
1. **Isolate the \(y\)-term:**
\[
-2x + 2y = 16 \quad \Rightarrow \quad 2y = 2x + 16
\]
2. **Solve for \(y\):**
\[
y = \frac{2x + 16}{2} \quad \Rightarrow \quad y = x + 8
\]
So, the slope-intercept form of the equation is:
\[
\boxed{y = x + 8}
\]
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Simplify this solution Extra Insights
To rewrite the equation \(-2x + 2y = 16\) in slope-intercept form (which is \(y = mx + b\)), we need to solve for \(y\). First, add \(2x\) to both sides: \[ 2y = 2x + 16 \] Now, divide every term by \(2\): \[ y = x + 8 \] So, the slope-intercept form of the equation is \(y = x + 8\).
