Question

Which statements are true about the graph of y ≤ 3x + 1 and y ≥ –x + 2? Check all that apply.

The slope of one boundary line is 2.
Both boundary lines are solid.
A solution to the system is (1, 3).
Both inequalities are shaded below the boundary lines.
The boundary lines intersect.

Answer 1

True:
- Both boundary lines are solid. (Inequalities are ≤ and ≥, so boundaries included.)
- A solution to the system is (1, 3). (3 ≤ 3(1)+1 = 4 and 3 ≥ −1+2 = 1.)
- The boundary lines intersect. (Lines y = 3x+1 and y = −x+2 have different slopes, meet at x = 1/4.)

False:
- The slope of one boundary line is 2. (Slopes are 3 and −1.)
- Both inequalities are shaded below the boundary lines. (y ≤ ... is shaded below, y ≥ ... is shaded above.)