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 line \( y = 3x \)

The region for \( y\circ3x \) and \( x\circ - 2 \) is the overlapping (purple) region. For the line \( y = 3x \), the shaded region is above the line (since the purple region is above the red line \( y = 3x \)), so the inequality for \( y\) and \( 3x \) should be \( y\geq3x \) (the line is solid, so we use \(\geq\) or \(\leq\); since it's above, \(\geq\)).

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

The line \( x = - 2 \) is a vertical line. The shaded region is to the right of \( x=-2 \) (since the purple region is to the right of the blue line \( x=-2 \)), and the line is solid, so the inequality for \( x\) and \( - 2 \) should be \( x\geq - 2 \) (to the right of \( x=-2 \) and the line is solid, so \(\geq\)).

So the symbol that works for both is \(\geq\).

Answer:

\(\geq\) (the option with \(\geq\))