1. **State the problem:** Find the inverse function of $ f(x) = \frac{3}{5}x - 12 $ in slope-intercept form $ y = mx + b $. 2. **Recall the formula and rules:** To find the inverse function, swap $ x $ and $ y $ and then solve for $ y $. 3. **Start with the original function:** $$ y = \frac{3}{5}x - 12 $$ 4. **Swap $ x $ and $ y $:** $$ x = \frac{3}{5}y - 12 $$ 5. **Solve for $ y $:** Add 12 to both sides: $$ x + 12 = \frac{3}{5}y $$ 6. **Isolate $ y $ by dividing both sides by $ \frac{3}{5} $:** $$ y = \frac{x + 12}{\frac{3}{5}} $$ Use the reciprocal to divide: $$ y = (x + 12) \times \frac{5}{3} $$ 7. **Distribute $ \frac{5}{3} $:** $$ y = \frac{5}{3}x + \frac{5}{3} \times 12 $$ Calculate $ \frac{5}{3} \times 12 = 20 $: $$ y = \frac{5}{3}x + 20 $$ 8. **Final answer:** $$ f^{-1}(x) = \frac{5}{3}x + 20 $$ This is the inverse function in slope-intercept form.