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Question 81519This question is from textbook beginners algebra
: Could your graph this inequality please, I am stuck
3x-4y<12
This question is from textbook beginners algebra
Answer by mathdoc316(9)   (Show Source):
You can put this solution on YOUR website!
I don't know if you are stuck with graphing a line 3x-4y=12 or if you are stuck graphing the inequality 3x-4y<12 after that is done
To graph the line 3x-4y=12 you note the y intercept is (4,0) and the x intercept is (0,-3). The slope is -3/4. Draw a line through the x and y intercepts. My line here is not very exact or straight - I think you can
do better!
^
| X
X4
P X |
X +3
X |
X +2
X |
X +1
X |
<--|---X---|---|---|---|---|---|---|-->
-4 X-3 -2 -1 0 1 2 3 4
X |
X Q + -1
|
+ -2
|
+ -3
|
+ -4
|
v
Notice the line divides the area of the graph into two parts
One part lies above the line and to the left. For example see point P I have labeled. If you go horizontally to the right, you hit the line - the x value is larger on the line than it is at point P. If you go vertically down, you come to the line again - the y value is smaller on the line than it is on P. That is true for all points P on that side of the line. For a point Q below the line and to the right of it, the X value is larger and the Y value is smaller.
One one side of the line it is going to be true that 3x - 4y < 12
That is the side you want to shade with ///// on your graph
On the other side of the line it is going to be true that 3x - 4y > 12
That is the side you want to leave alone and not shade it
My feeling for the expression 3x - 4y is that it will be smaller if x is smaller or if y is bigger. In other words, to the left of the line or above it, where P is
You can check this by putting in some numbers where P might be like maybe
x=-4, y = +4
is 3x - 4y < 12 ?
-12 - 16 = -28 < 12 YES
so P is in the area you want to shade.
I hope this explains it thoroughly for you!
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