Jim : ) 1. determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following inequality: y < two thirdsx + 2 the origin is not included in the shaded region and the shaded area is above the line. the origin is not included in the shaded region and the shaded area is below the line. the origin is included in the shaded region and the shaded area is above the line. the origin is included in the shaded region and the shaded area is below the line.

Problem 1

Plug (x,y) = (0,0) into the inequality
y < (2/3)x + 2
0 < (2/3)*0 + 2
0 < 0 + 2
0 < 2
The last inequality is true so we do shade the entire region that has the origin in it. In other words, the origin is in the shaded region. For this function, the origin is below the boundary line so the shaded region is below the line

choice D



Problem 2

x = number of liters of fruit syrup
y = number of liters of water

"The total number of liters of syrup (x) and water (y) is 7 liters" so x+y = 7 which leads to y = -x+7

This graph is the line through (0,7) and (7,0). Every choice seems to have this graph shown.

"Three times the number of liters of water he mixed was 6 more than twice the number of liters of syrup" so we have the equation 
3x = 2y+6
which solves to
y = (3/2)x - 3
This line goes through the points (0,-3) and (2,0)

Choice D looks cut off but it looks like choice D is the answer as its the only one with (0,-3) on the line