#1**+2 **

Since this is a dashed line.....we will have either "< " or " > "

The points (3,1) and (1, -2) are on the graph boundary

The slope of this dashed line is [ -2 - 1 ] / [ 1 - 3 ] = -3 / -2 = 3 /2

The equation of the dashed line is

y = (3/2)( x - 1) - 2

y = (3/2)x - 3/2 - 2

y = (3/2)x - 7/2

We will either have

y < (3/2)x - 7/2 or y > (3/2)x - 7/2

(0 ,0) is in the feasible [ yellow ] region

Putting this coordinate into the second equation makes this inequality true

So....the inequality is

y > (3/2)x - 7/2 multiply through by 2

2y > 3x - 7 subtract 2y from both sides

0 > 3x - 2y - 7 which is the same as

3x - 2y - 7 < 0

CPhill
Oct 18, 2018