pre algebra help

Question

Elon sat on the dock with his fishing rod when suddenly he felt the rod being pulled down! He reeled in his catch, causing it to ascend at a constant rate of 0.1 meters per second. When it reached the water's surface after 35 seconds, Elon found it was only an old shoe.

Graph the relationship between the shoe's altitude (in meters relative to the water's surface) and time (in seconds).

Answer 1

The graph would have a vertical axis for distance (0 = water level) and a horizontal axis for time. The graph is linear (straight line) because the shoe is coming up at a constant rate of 0.1 m/sec. Distance = rate x time, so if it took 35 sec to land the shoe, it must have been hooked at a depth of 0.1 x 35 = -3.5 meters (negative because it's below the water level). This is your y-intercept (b in the standard linear equation of y = mx + b) The m, or slope, in this case is a positive 0.1 m/sec. (the line rises to the right as the shoe rises through the water over time).

The equation is d = 0.1t - 3.5 where d is the distance below water level and t is the time he spent reeling in the shoe. You can see that when t = 0, the shoe is still at the 3.5m depth, and when t = 35, d = 0 (at the surface).