Example 3 Write each equation in slope-intercept form. 5 y-2=-(4)/(3)(x+6)

## Step 1<br />The given equation is \(y-2=-\frac{4}{3}(x+6)\). The slope-intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.<br /><br />## Step 2<br />To convert the given equation into slope-intercept form, we need to distribute the \(-\frac{4}{3}\) across the terms in the parentheses.<br /><br />### \(y-2=-\frac{4}{3}x-\frac{4}{3}*6\)<br /><br />## Step 3<br />Simplify the equation by multiplying \(-\frac{4}{3}\) with 6.<br /><br />### \(y-2=-\frac{4}{3}x-8\)<br /><br />## Step 4<br />Finally, add 2 to both sides of the equation to isolate \(y\).<br /><br />### \(y=-\frac{4}{3}x-6\)