Final answer:
The correct linear equation to model the distance the driver is from home as they drive towards it is d = 450 - 42t, which represents the starting distance minus the distance covered over time, in slope-intercept form.
Step-by-step explanation:
When creating a linear equation to model the distance a driver is from home, we assign variables to represent the distance (d) and time (t), and identify the starting distance and rate of change. In this scenario, the driver starts 450 miles from home (d = 450 when t = 0), and the distance from home decreases by 42 miles for each hour driven (42 miles/hour). Thus, the change in distance over time can be represented as a decrease of 42 miles for each hour, leading to the equation d = 450 - 42t, which is in slope-intercept form (y = mx + b) where d corresponds to y, -42 is the slope (m), and 450 is the y-intercept (b).