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 ○ 3x
x ○ −2
options: ≤, ≥, <, >

Explanation:

Step1: Analyze the x - inequality

The vertical line is \(x = - 2\). The shaded region for the \(x\) - related inequality is to the right of \(x=-2\) (since the blue region is on the right of \(x = - 2\)). So the inequality for \(x\) should be \(x>-2\).

Step2: Analyze the y - inequality

The line \(y = 3x\) (since the slope of the line passing through \((0,0)\) and \((1,3)\) is \(m=\frac{3 - 0}{1 - 0}=3\)). The shaded region for the \(y\) - related inequality is above the line \(y = 3x\) (the purple region is above the red line \(y = 3x\)). So the inequality for \(y\) should be \(y>3x\).

Answer:

\(>\)