The system of inequalities represented by the graph is y ≥ x - 2, y < -3x - 6
What system of inequalities is represented by the graph?
From the question, we have the following parameters that can be used in our computation:
The graph
A linear equation is represented as
y = mx + c
Where
c = y-intercept i.e. c = y, when = 0
Considering the dotted lines, we have the following points
(0, -6) and (-2, 0)
So, e have
y = mx - 6
Using the point (-2, 0), we have
-2m - 6 = 0
m = -3
So, we have
y = -3x - 6
The inequality is a dotted line, shaded to the left
So, we have
y < -3x - 6
Considering the closed lines, we have the following points
(0, -2) and (-4, -6)
So, e have
y = mx - 2
Using the point (-4, -6), we have
-4m - 2 = -6
-4m = -4
m = 1
So, we have
y = x - 2
The inequality is a closed line, shaded to the right
So, we have
y ≥ x - 2
Hence, the system of inequalities is y ≥ x - 2, y < -3x - 6