SOLUTION: 2x is greater or equal to y. I'm not sure how to graph it.

Algebra ->  Inequalities -> SOLUTION: 2x is greater or equal to y. I'm not sure how to graph it.      Log On


   

Question 114567This question is from textbook Mathematics with Applications
: 2x is greater or equal to y. I'm not sure how to graph it. This question is from textbook Mathematics with Applications

Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
2x+%3E=+y
Or
y%3C=2x

Think about how you've done inequalities on the number line. For instance, they'd ask you to graph something like x > 2 or y<2
greater than" meant "everything off to the right" on the number line

less than" meant "everything off to the left" the number line

now do your inequality:
y%3C=2x
the first step is to find the "equals" part, or y=2x
then graph it

Solved by pluggable solver: Graphing Linear Equations
In order to graph y=2%2Ax%2B0 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-4

y=2%2A%28-4%29%2B0

y=-8%2B0 Multiply

y=-8 Add

So here's one point (-4,-8)




Now lets find another point

Plug in x=-3

y=2%2A%28-3%29%2B0

y=-6%2B0 Multiply

y=-6 Add

So here's another point (-3,-6). Add this to our graph





Now draw a line through these points

So this is the graph of y=2%2Ax%2B0 through the points (-4,-8) and (-3,-6)


So from the graph we can see that the slope is 2%2F1 (which tells us that in order to go from point to point we have to start at one point and go up 2 units and to the right 1 units to get to the next point) the y-intercept is (0,0)and the x-intercept is (0,0)


We could graph this equation another way. Since b=0 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,0).


So we have one point (0,0)





Now since the slope is 2%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,0), we can go up 2 units



and to the right 1 units to get to our next point


Now draw a line through those points to graph y=2%2Ax%2B0


So this is the graph of y=2%2Ax%2B0 through the points (0,0) and (1,2)



You have already graphed the "or+equal+to" part (it is just the line);

now you are ready to do the "y_+less_+than" part; it means, this is where you need to shade+one+side of the line or+the+other.
All you need to be sure is do you need y+LESS THAN the line, do you need ABOVE the line, or BELOW the line?
Naturally, you want below the line. So shade it in: the LINE and BELOW the line.
the side you shaded is the "solution region"