b To graph the inequalities we will graph the boundary lines first. Then we will test a point to check which region to shade.
Boundary lines
To graph the boundary lines, we will treat the inequalities as equations. Therefore, we want to graph the following functions.
y= 3x-4 and y = - x+4
Let's determine the slopes and the y-intercepts of these equations!
Feature
y=3x-4
y=- x+4
Slope
3
-1
y-intercept
-4
4
Now we can plot the boundary lines!
Testing a Point and Graphing
Let's test the point (0,0) to see which regions we must shade. We will start with inequality A.
We can tell that the point (0,0) does not satisfy our inequalities. Therefore, in each case we will shade the region that does not contain the point (0,0).
c The overlapping region is where both inequalities are satisfied. Therefore, it represents the solutions that make both inequalities A and B true.
