Question

On a coordinate plane, 2 straight lines are shown. The first solid line is horizontal at y = -1. Everything above the line is shaded. The second dashed line has a negative slope and goes through (-2, 1) and (0, 0). Everything below the line is shaded. A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. Which constraint could be part of the scenario?

1) The pool is 1 meter deep.
2) The pool is 2 meters deep.
3) The toy falls at a rate of at least -1/2 meter per second.
4) The toy sinks at a rate of no more than -1/2 meter per second.

Answer 1

The constraint that could be part of the scenario is that the toy sinks at a rate of no more than -1/2 meters per second.

Step-by-step explanation:

The constraint that could be part of the scenario is: The toy sinks at a rate of no more than -1/2 meters per second.

Since the second dashed line on the coordinate plane has a negative slope, it indicates that the toy is sinking at a certain rate. The slope of the line represents the rate of change of y (depth) with respect to x (time). In this case, the slope is negative, indicating that the toy is sinking.

However, the constraint states that the toy sinks at a rate of no more than -1/2 meters per second. This means that the rate of change of depth must be less than or equal to -1/2 meters per second. By incorporating this constraint into a system of inequalities, the depth of the toy can be determined depending on the time since it was dropped.