Choose the system of inequalities that matches the graph below.

Question

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

After plotting each line, find the equation of each line.
Reading the y-intercept and finding the slope is straight forward.

 

See http://www.hwmath.net/dev/alg/inequal1220.jpg

Next, the equations shown are for the boundary lines and they are written in slope intercept form. The solid line means that the line is part of the solution and the dashed line means that the line is NOT part of the equation.

The green area shows where both inequalities are true
So y < x -1 and y >= -4x + 9.

These inequalities can be re-written algebraically as

  y - x <  -1   and y + 4x >= 9

 

by moving the x-term of each equation from the right side of the inequality to the left. Can you follow that step and select the answer that matches your choices?