1. **Problem statement:** We need to write a linear function for the distance $d$ (in miles) the plane is from its destination $t$ hours after reaching cruising altitude, given the initial distance is 3400 miles and the plane travels at 500 miles per hour. 2. **Formula and explanation:** The distance from the destination decreases as time passes. The general linear function for distance remaining is: $$d = d_0 - rt$$ where $d_0$ is the initial distance, $r$ is the rate (speed), and $t$ is time. 3. **Substitute values:** Here, $d_0 = 3400$ miles and $r = 500$ miles/hour, so: $$d = 3400 - 500t$$ 4. **Calculate distance after 2 hours:** Substitute $t=2$: $$d = 3400 - 500 \times 2 = 3400 - 1000 = 2400$$ 5. **Interpretation:** After 2 hours, the plane is 2400 miles from its destination. **Final answers:** - Linear function: $d = 3400 - 500t$ - Distance after 2 hours: 2400 miles