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# thank you for the help

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thank you for the help

Aug 22, 2018

#1
+101161
+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

Aug 23, 2018
#2
+101161
+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

Aug 23, 2018
#3
+101161
+2

Last one

The point  (0, 3) = (x, y)  is in the shaded area

Notice  that  y - x  < 0   is not true so the first and last answers can be eliminated

And  in the third answer  y ≤ 1 is not true, either