#1**+2 **

First one

y < -(3/4)x + 1

This graph will have a negative slope and will be a dashed line going through the y intercept of -1

y > (2/3)x - 3

This graph will be a dashed line with a positive slope and going through the y intercept of - 3

Thus....either graph on the top right or the one on the bottom right are correct

Pick a point say (0, 0) = (x , y)

Notice that this point will satisfy both inequalities

Since this point is in the shaded region of the one on the bottom right...thus...this one is correct

CPhill
Aug 23, 2018

#2**+2 **

Second one

2x + y ≥ -4 rearrange as

y ≥ -2x - 4

This graph is a solid line with a positive slope and a y intercept of -4

y ≥ 2x

This is a solid line with a positive slope going through the origin

y - 3 > (1/2)x

y > (1/2) x + 3

This is a dashed line with a positive slope and a y intercept of 3

Thus the graphs on the top right and bottom left can be eliminated since they contain lines with negative slopes

Pick the point (0, 6) = (x , y )

Notice that this point will satisfy all three inequalities

Since this point is in the shaded area of the graph on the bottom right and not in the shaded area of the graph on the top left, then the graph on the bottom right must be correct

CPhill
Aug 23, 2018