1. **State the problem:** We are given that the temperature $y$ in degrees Fahrenheit is a linear function of the number of cricket chirps $x$. When $x=40$, $y=50$, and when $x=80$, $y=60$. We want to find the equation of this linear function. 2. **Recall the formula for a linear function:** $$y = mx + b$$ where $m$ is the rate of change (slope) and $b$ is the initial value (y-intercept). 3. **Given information:** - Rate of change $m = \frac{1}{4}$ - Initial value $b = 40$ 4. **Write the equation using the given values:** $$y = \frac{1}{4}x + 40$$ 5. **Verify with given points:** - For $x=40$: $$y = \frac{1}{4} \times 40 + 40 = 10 + 40 = 50$$ - For $x=80$: $$y = \frac{1}{4} \times 80 + 40 = 20 + 40 = 60$$ This matches the given data, so the equation is correct. **Final answer:** $$y = \frac{1}{4}x + 40$$