Question

hich 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 are included.)
- A solution to the system is (1, 3). (Check: 3 ≤ 3(1)+1 = 4 and 3 ≥ −1+2 = 1.)
- The boundary lines intersect. (Solve 3x+1 = −x+2 → 4x = 1 → x = 1/4, y = 7/4.)

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