Choose the system of inequalities that matches the graph below.

Question

Choose the system of inequalities that matches the graph below.

coordinate plane with a solid line through points (0, 9) and (1, 5). A dashed line passes through points (0, -1) and (1, 0). There is yellow shading above the solid line and blue shading below the dashed line. The shading turns green in the overlap.

 

 

Choose one answer.
A. 4x + y<(line underneath) 9
x - y < 1
 

B. 4x + y < 9
x - y<(line underneath) 1
 

C. 4x + y>(line underneath) 9
x - y > 1 
 

D. 4x + y > 9
x - y>(line underneath) 1

Answer 1

May,

 

The answer is D.  

 

To see this, use m = (y₂ - y₁)/(x₂ - x₁) to find the slopes of the solid and dashed lines, and x=0 in y=mx + b to find b, the y-intercepts for both lines.

 

You get:

Solid line:      y = -4x + 9  or (4x + y) = 9 for points on the line;

                      then for any x, all y such that (4x + y) > 9 are above the solid line.

 

Dashed line:   y = x -1 for points on the dashed line;

                      then for any x, all y such that (x - y) > 1 are below the dashed line.

 

And when you satisfy both those inequalities simultaneously, y is both above the solid line and below the dashed line, so in the green zone.