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: Identify the blue - line inequality

The blue - line is a horizontal line at $y = 2$. The shaded region below the blue line represents $y\leq2$.

Step2: Identify the red - line inequality

The red - line has a negative slope. Let's assume the equation of the line is $y=mx + b$. The line passes through points (0, 2) and (2, - 4). First, find the slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-4 - 2}{2-0}=\frac{-6}{2}=-3$. Using the point - slope form with the point (0, 2), the equation of the line is $y=-3x + 2$. The shaded region below the red line represents $y\leq - 3x+2$.

Answer:

The system of inequalities is $y\leq2$ and $y\leq - 3x + 2$