Question

Select the inequality that corresponds to the given graph.

Answer 1

2x - 5y -10

x - y > 3

2x - y < -4

x + 2y -8

Answer 2

Before I begin could you check the first and fourth answers to see if they have equal signs or inequality signs?

Answer 3

x+2y-8 put that into slope intercept form (y=mx+b)

Answer 4

oh my bad, the first one is 2x - 5y is greater than or equal to -10
and the last answer is x + 2y is greater than or equal to -8

Answer 5

b will then represent your y intercept of -4 as show in the graph you posted. Over 2, up 1. over 2, up 1, repeat

Answer 6

Let's start with the concept. Begin by doing as graham said and isolating the y value.
We can eliminate the middle two answers because the line ISN'T dotted. If the line is NOT dotted, it means that it has to be GREATER/LESS THAN OR EQUAL TO.

Answer 7

<= means greater than or equal to

We can do two things from here. Since both are greater than or equal to, we don't have to worry about signs and plug in values for 2x - 5y=-10 and x + 2y=-8.

The graph crosses the x-axis when x=-8 and y=0. Plugging this into both equations we get
2(-8)-5(0)=-10 and (-8)+2(0)=-8.
We get for the first one -16<=-10. That doesn't work.
For the second -8=-8. This answer works! x+2y<=8 is your answer.

Answer 8

Alternatively, let's do the normal way.
We have 2x - 5y<=-10 and x + 2y<=-8.
Get y alone for both equations. The sign changes when we divide or multiply by negative numbers.
2x - 5y>=-10 x + 2y>=-8.
-5y>=-10-2x 2y>=-8-x
y<=2+2x/5 y>=-4-x/2
When y is greater than something, you shade above it, when y is less than something you shade below it. You can check it by plugging in x=-8 and see if you get 0, just like the graph shows.

For my previous answer I accidentally wrote less than or equal to instead of greater than or equal to. Hope this helps!

Answer 9

thank you so much : ) !