Question

Which inequality will have a shaded area below the boundary line? A. y - x > 5 B. 2x - 3y < 3 C. 2x - 3y < 7 D. 7x + 2y < 2 E. 3x + 4y > 12

Answer 1

When you change the inequality as the formula of y>ax+b, it is over the boundary line. While the formula is y<ax+b, it is below the boundary line. So we can get the answer is D.

Answer 2

Answer:
D. 7x + 2y < 2

Step-by-step explanation:
The two general forma of the inequality are:
y < mx + c .........> In this case, shading is below the boundary line
y > mx + c .........> In this case, shading is above the boundary line

Since we are looking for the inequality with shading below the boundary line, therefore, we are looking for an y < mx + c format

Now, let's check the givens:
y - x > 5
Rearranging, we would get:
y > x + 5
The shading is above the boundary line. This option is incorrect

2x - 3y < 3
Rearranging, we would get:
2x - 3 < 3y
The shading is above the boundary line. This option is incorrect

2x - 3y < 7
Rearranging, we would get:
2x - 7 < 3y
The shading is above the boundary line. This option is incorrect

7x + 2y < 2
Rearranging, we would get:
2y < -7x + 2
The shading is below the boundary line. This option is correct

3x + 4y > 12
Rearranging, we would get:
4y > -3x + 12
The shading is above the boundary line. This option is incorrect

As a second solution, I attached the graphs of the 5 given functions.
Observing these graphs, we will find that the correct one is D

Hope this helps :)