The system of inequalities in the graph is:
y ≥ (1/2)x - 1
y < -3x + 1
How to find the system of inequalities?
First we need to find the two lines.
First the line with positive slope, remember that the general equation of a line is:
y = ax + b
Where a is the slope and b is the y-intercept.
We can see that the line crosses the y-axis at y = -1, so:
y = ax - 1
It also passes through (2, 0), then:
0 = a*2 - 1
1 = 2a
1/2 = a
And the region shaded is above the line, and the line is solid, so we can write:
y ≥ (1/2)x - 1
The other inequality is a dashed line and the region shaded is below the line.
the y-intercept in this case is: y = 1
y = ax + 1
And it also passes through (1, -2), so:
-2 = a*1 + 1
-2 - 1 = a
-3 = a
The inequality is:
y < -3x + 1
The system is:
y ≥ (1/2)x - 1
y < -3x + 1