Step-by-step explanation:
|x + 5| ≥ y – 2
First we replace the inequality sign by = sign
|x + 5| = y – 2
solve for y and then graph it
add 2 on both sides
y = |x + 5|+ 2
Equation is in the form of y=a|x-h|+k
where (h,k) is the vertex
h = -5 and k = 2
So vertex is (-5,2)
Now make a table
x y = |x + 5|+ 2
-10 y = |-10+5| + 2= 7
-5 y = |-5+5| + 2= 2
0 y = |0+5| + 2= 7
Now plot all the points we got the table and graph it
Now we do shading
Lets pick any point inside the V shaped graph and check with our inequality
LEts pick (-5,5)
|x+5| ≥ y – 2
plug in -5 for x and 5 for y
|-5+5| ≥ 5– 2
0 > = 3, its false
So we cannot shade the part containing (-5,5)
we shade the bottom part on graph
the graph is attached below
