Question

Write down the two inequalities that

describe the unshaded region in the
diagram below.
-3 -2 -1
Y
7
6-
-5-
4,
37
2-
1+
0
-1.
-2-
-3+
1
-2
3
-50
-6
7
x

Answer 1

Explanation:

first, we find the line equations for the separating lines.

these we then turn into inequalities based on the shading (or rather not-shading) and the fact that the lines are solid or dotted.

the solid line has a slope of 2 (for every increase of x by 1, y increases by 2) and a y-intercept at 3. so, its equation is

y = 2x + 3

the dotted line has a slope of -1 (for every increase of x by 1, y decreases by 1) and a y-intercept at 4. so, its equation is

y = -x + 4

the unshaded region for the solid line is below the line. so, the inequality for that is the value of all y smaller than the line equation numbers. and the line is solid, so it is included in the valid values :

y <= 2x + 3

the unshaded region for the dotted line is above the line.

so, the inequality for that is the value of all y larger than the line equation numbers. and the line is dotted, so it is not included in the valid values :

y > -x + 4