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

Explanation:

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

The line \(y=3x\) is a solid line. The shaded region is above the line \(y = 3x\). For a linear inequality \(y\) and \(y=mx + b\), if the line is solid (\(\leq\) or \(\geq\)) and the region is above \(y=mx + b\), the inequality is \(y\geq mx + b\). Here \(m = 3\) and \(b=0\), so \(y\geq3x\).

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

The line \(x =- 2\) is a solid line. The shaded region is to the right of \(x=-2\). For a vertical line \(x = a\), if the line is solid (\(\leq\) or \(\geq\)) and the region is to the right of \(x=a\), the inequality is \(x\geq a\). Here \(a=-2\), so \(x\geq - 2\).

Answer:

\(\geq\) (the symbol \(\geq\) should be written in both circles)