The area shaded with horizontal lines is the solution set of the inequalities;

Shushino

1 year ago

To determine which set of inequalities corresponds to the shaded region, let's analyze the graph and the given options.

1. Identifying the lines:
The line
𝑦
=
𝑥
y=x has a positive slope and passes through the origin.
The line
𝑦
+
2
𝑥
=
−
3
y+2x=−3 (or
𝑦
=
−
2
𝑥
−
3
y=−2x−3) has a negative slope and intersects the y-axis at
−
3
−3.
The line
𝑥
=
3
x=3 is a vertical line passing through
𝑥
=
3
x=3.
2. Analyzing the shaded region:
The shaded region is below the line
𝑦
=
𝑥
y=x, so
𝑦
≤
𝑥
y≤x.
The shaded region is above the line
𝑦
=
−
2
𝑥
−
3
y=−2x−3, so
𝑦
≥
−
2
𝑥
−
3
y≥−2x−3.
The shaded region is to the left of the line
𝑥
=
3
x=3, so
𝑥
≤
3
x≤3.
3. Matching the inequalities:
Given this analysis, the inequalities that describe the shaded region are:

𝑦
≤
𝑥
,
𝑦
≥
−
2
𝑥
−
3
,
𝑥
≤
3
y≤x,y≥−2x−3,x≤3
This corresponds to option B:

B.
𝑦
≤
𝑥
y≤x,
𝑦
+
2
𝑥
≥
−
3
y+2x≥−3,
𝑥
≤
3
x≤3.

yinkajewole

12 years ago

this answer is 1/9 which is A.