1. **Problem:** Marty’s heart rate is 168 beats per minute after exercising and decreases by 4 beats per minute until it reaches his resting heart rate of 72 beats per minute. We need to find how many minutes it takes for his heart rate to return to resting. 2. **Formula:** Use the linear rate of change formula: $$\text{Final heart rate} = \text{Initial heart rate} - (\text{rate of decrease} \times \text{time})$$ 3. **Set up the equation:** $$72 = 168 - 4t$$ 4. **Solve for $t$:** $$4t = 168 - 72$$ $$4t = 96$$ 5. **Divide both sides by 4:** $$t = \frac{\cancel{4}t}{\cancel{4}} = \frac{96}{4}$$ 6. **Calculate:** $$t = 24$$ **Answer:** Marty’s heart rate returns to resting after 24 minutes. --- 1. **Problem:** Find the equation of a line with slope $-\frac{1}{4}$ passing through point $(8, 12)$. 2. **Formula:** Use point-slope form: $$y - y_1 = m(x - x_1)$$ where $m$ is slope, $(x_1, y_1)$ is the point. 3. **Substitute values:** $$y - 12 = -\frac{1}{4}(x - 8)$$ 4. **Distribute slope:** $$y - 12 = -\frac{1}{4}x + 2$$ 5. **Add 12 to both sides:** $$y = -\frac{1}{4}x + 2 + 12$$ $$y = -\frac{1}{4}x + 14$$ **Answer:** The equation is $y = -\frac{1}{4}x + 14$.