Question 1182456: Determine whether each ordered pair is a solution to the inequality y>−2x−4.
(0,1)
(3,10)
(4,9)
(7,−5)
(−2,−9)
Thank you!
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52790)   (Show Source):
You can put this solution on YOUR website! .
For each pair, consider the second number as the left side of the inequality;
calculate the right side with the first number of the pair;
then compare the left and the right side.
For example, with the first pair:
- the left side is 1;
- the right side is -2*0 - 4 = -4.
The inequality takes the form
1 > - 4.
Is it TRUE ? - - - - - - - - ANSWER : YES, is it true.
ANSWER. The first pair satisfies the given inequality.
Doing this way, you can check all other pairs on your own.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Let's plug the x,y coordinates of choice A into the inequality
So we'll plug in x = 0 and y = 1
y > -2x-4
1 > -2(0)-4
1 > 0-4
1 > -4
The last inequality shown above is true because 1 is indeed larger than -4, ie, 1 is to the right of -4 on the number line.
So (0,1) is a solution.
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Now let's try the coordinates for point B
y > -2x-4
10 > -2(3)-4
10 > -6-4
10 > -10
This is also true, so point B is also a solution point.
This process is repeated for choices C through E.
You should find that points A through D are all solution points. Only point E is not a solution.
Effectively, the answer is everything but choice E.
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Check out the graph below. The graph of y > -2x-4 consists of the dashed boundary line y = -2x-4. This line goes through the two points (0,-4) and (1, -6).
The shaded region is above the boundary. The dashed boundary line visually means "points on the boundary are not solutions". If you want boundary points to be solutions, then you would need to add on an "or equal to". In other words, you would need to graph  to have a solid boundary line and have points on the boundary count as solutions.
Graph:
We can see that points A through D are in the blue solution region, which is above the dashed boundary line. Point E is the only non-solution outside this blue region. I used GeoGebra to make the graph.
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