Question

Write a system of inequalities for the graph shown to the right.
%
10

Answer 1

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 =
`\[ m = (5 - (-5))/(5 - 0) = (10)/(5) = 2 \]`

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.