Final answer:
The graph of Rachel's position as a function of time would be a straight line with a constant slope (her velocity) and a y-intercept of zero since she starts at her house. The algebraic expression would be y = mx + b, with b equal to zero.
Step-by-step explanation:
To graph Rachel's position as a function of time, one would plot time on the horizontal axis (x-axis) and the distance from home on the vertical axis (y-axis). Assuming Rachel starts at her house, the y-intercept would be zero, indicating that her initial distance from home at time zero is zero meters.
The slope of the graph represents Rachel's velocity since it’s the change in position over time (rise over run). If Rachel maintains a constant rate, this graph would be a straight line with a constant slope. The algebraic expression for this linear function would be y = mx + b, where m is the slope (or the constant velocity in this case) and b is the y-intercept, which is zero in this scenario.
This is also stated in Physics as the equation x = xo + ut, where xo is the initial position (y-intercept), u is the average velocity (slope), and t is time.