Answer:
Option 1
Step-by-step explanation:
In each inequality we have the equation of a line.
The first step in solving this problem is to identify each line in the figures.
To do this, we willient your cut points.
y = x-2
We do y = 0
0 = x-2
x = 2. This line cuts the x-axis at x = 2.
Now we do x = 0
y = -2.
This line cuts the y-axis in y = -2.
Now we can identify this line in the figure.
The inequality is:
y≤x - 2
Then the region that represents this inequality are all the points below the line y = x-2 and also those that belong to the line.
Try for example the point (0, -4) that is below this line.
-4≤0-2
-4≤-2. The inequality is met.
We do the same for the other line:
y<-3x - 2
y = -3x-2.
The cut points are:
2 = -3x
x = -2 / 3
y = -2
Locate in the graphs the line that meets these characteristics.
The region understood by this inequality are all points below the line
y = -3x-2 and which, in turn, are below the line y = x-2.
Once again, the point (-4.0) complies with both inequalities.
Identify these characteristics in the options, and you will see that the correct option is the first
