Question

2 Points

Let y = 3t+ 6 be a linear function representing the distance, in feet, from
home for an ant t minutes after starting out from a location near its home.
What does the number 3 represent in this function?

Answer 1

In the given function, y = 3t+ 6, the number 3 represents the rate of change or slope of the linear function. It tells us that for every one unit increase in time (in minutes), the distance covered by the ant increases by 3 units (in feet). In other words, the slope of the line represents the speed or rate at which the ant is traveling away from its home. The coefficient of t in the equation is thus the slope of the line and represents the change in distance per unit change in time. In this case, it means that the ant is moving away from its home at a constant rate of 3 feet per minute.