7. Rewrite in slope-intercept form: \[-2 x+2 y=16\]

To rewrite the equation \(-2x + 2y = 16\) in slope-intercept form (which is \(y = mx + b\)), start by isolating \(y\). First, add \(2x\) to both sides: \[2y = 2x + 16.\] Next, divide every term by 2: \[y = x + 8.\] Now you have the slope-intercept form, where the slope \(m\) is 1 and the y-intercept \(b\) is 8. Transforming equations into slope-intercept form can make it easier to graph linear functions. In this case, the slope of 1 means for every unit you move right on the x-axis, you move up 1 unit on the y-axis, indicating a diagonal line rising from left to right. Many students commonly make the mistake of forgetting to divide all terms when isolating \(y\), which can lead to incorrect values for slope and intercept. Double-check your arithmetic and remember that every term must be treated equally to preserve the balance of the equation!