The system of inequalities for the graph shown is: B. y ≥ -5x + 5, y < 2x - 5.
How to write the system of inequalities?
The slope of the red dashed line = change in y / change in x =
![\[ m = (5 - (-5))/(5 - 0) = (10)/(5) = 2 \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/knvwb43htqbcinn8bx0n56og4kgs37ttfy.png)
The red line is dashed and the shaded portion is below it, we will use the sign "<", and since it intercepts the y-axis at y = -5, the y-intercept is -5. Therefore, the inequality for the red line is:
y < 2x - 5.
The slope of the blue solid line (m) = -5/1 = -5.
The blue line solid and the shaded portion is above it, we will use the sign "≥", and since it intercepts the y-axis at y = 5, the y-intercept is 5. Therefore, the inequality for the red line is:
y ≥ -5x + 5.
The system is: B. y ≥ -5x + 5, y < 2x - 5.