Question

a system of inequalities, where x is the rate of a spaceship in a video game and y is where the ship travels on the screen in 3.5 seconds, is represented by the graph. which symbol could be written in both circles in order to represent this system algebraically? y o 3x x o -2

Explanation:

Step1: Analyze the line \(y = 3x\)

The shaded region above the line \(y=3x\) (the blue - shaded area) implies \(y\geq3x\). We know that if the shaded region is above the line \(y = mx + b\) (where \(m = 3\) and \(b = 0\) in this case), the inequality is \(y\geq mx + b\).

Step2: Analyze the line \(x=-2\)

The shaded region to the right of the vertical line \(x = - 2\) implies \(x\geq - 2\). For a vertical line \(x = a\) (here \(a=-2\)), if the shaded region is to the right of the line, the inequality is \(x\geq a\).

Answer:

\(\geq\)