Question

Please help! posted picture of question

Answer 1

If you eliminate obvious wrong answers you increase your chances of getting the question correct.

Notice the inequality signs are both "equal to" which means a solid boundary line. This means choice B and D can not be correct.

You can test a point that is exclusively in the shaded region of each graph.

x + 2y ≤ 4
-x           -x    solve for y by moving x term
      2y ≤ -x + 4
       ÷2    ÷2   divide both sides of the inequality by 2
y ≤ -1/2x + 2 ← plot 2 on y-axis then move down 1 and right 2 put 2nd point
    shade below the solid line

3x - y ≥ 2 when solved for y → y ≤ 3x - 2 (the inequality sign switched because in the process of solving for y I had to divide by a negative number)

plot -2 on the y-axis then move up 3 and to the right 1 put 2nd point 
   shade below the line

the answer is choice A  only graph where they have shaded below both lines...use the y-intercept as a guide for shading above or below the line... shading where numbers are greater than the y-intercept is shading above the line and shading where numbers are less then the y-intercept is shading below the line