Put the following equation in slope-intercept form: $y-2=-\frac{2}{3}(x-1)$ \[ y= \]

Step 1 ：Given the equation: \(y-2=-\frac{2}{3}(x-1)\)

Step 2 ：Distribute the \(-\frac{2}{3}\) to both terms inside the parentheses: \(y-2=-\frac{2}{3}x+\frac{2}{3}\)

Step 3 ：Isolate y on one side of the equation: \(y=-\frac{2}{3}x+\frac{8}{3}\)

Step 4 ：\(\boxed{y=-\frac{2}{3}x+\frac{8}{3}}\) is the equation in slope-intercept form.