9. A car moving at a constant speed passes a timing device at \( t=0 \). After 8 seconds, the car has traveled 840 feet. What linear function in the form \( y=m x+b \) represents the distance in feet, \( d \), the car has traveled any number of seconds, \( t \), after passing the timing device?

To find the linear function representing the distance \( d \) traveled by the car over time \( t \), we first determine the slope \( m \). The car travels 840 feet in 8 seconds, so the slope is: \[ m = \frac{d}{t} = \frac{840 \text{ feet}}{8 \text{ seconds}} = 105 \text{ feet/second}. \] Since the car starts from the timing device (which we can consider as 0 feet at \( t=0 \)), the y-intercept \( b \) is 0. Putting it all together, the linear function is: \[ d(t) = 105t + 0 \] or simply \[ d(t) = 105t. \] This function shows how the distance varies linearly with time! Now, remember that this represents constant speed, which is why we have a straight line. The distance increases uniformly—just like that time you drove down a flat road at the same speed and felt like a racing champion!