SOLUTION: How do you solve and graph 3x-6y<12

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Question 99975: How do you solve and graph 3x-6y<12
Found 3 solutions by jim_thompson5910, fastblue, edjones:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph 3x-6y%3C12, we need to graph the equation 3x-6y=12 (just replace the inequality sign with an equal sign).
So lets graph the line 3x-6y=12 (note: if you need help with graphing, check out this solver)
+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+%281%2F2%29x-2%29+ graph of 3x-6y=12
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality 3x-6y%3C12 with the test point

Substitute (0,0) into the inequality
3%280%29-6%280%29%3C12 Plug in x=0 and y=0
0%3C12 Simplify



Since this inequality is true, we simply shade the entire region that contains (0,0)
Graph of 3x-6y%3C12 with the boundary (which is the line 3x-6y=12 in red) and the shaded region (in green)
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)

Answer by fastblue(13) About Me  (Show Source):
You can put this solution on YOUR website!
3x-6y<12
Solve for Y
Y = X/2 - 2
Graph the following, then Y < X/2 - 2
So the area under the curve not including the curve is the answer.

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
3x-6y<12
you can't solve it because you need 2 linear equations to solve for 2 variables.
you can graph it by getting points (x,y).
Ed
Solved by pluggable solver: Graphing Linear Equations


3%2Ax-6%2Ay=12Start with the given equation



-6%2Ay=12-3%2Ax Subtract 3%2Ax from both sides

y=%28-1%2F6%29%2812-3%2Ax%29 Multiply both sides by -1%2F6

y=%28-1%2F6%29%2812%29%2B%281%2F6%29%283%29x%29 Distribute -1%2F6

y=-12%2F6%2B%283%2F6%29x Multiply

y=%283%2F6%29%2Ax-12%2F6 Rearrange the terms

y=%281%2F2%29%2Ax-2 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=1%2F2 (the slope) and b=-2 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-8

y=%281%2F2%29%2A%28-8%29-2

y=-8%2F2-2 Multiply

y=-12%2F2 Add

y=-6 Reduce

So here's one point (-8,-6)





Now lets find another point

Plug in x=-6

y=%281%2F2%29%2A%28-6%29-2

y=-6%2F2-2 Multiply

y=-10%2F2 Add

y=-5 Reduce

So here's another point (-6,-5). Add this to our graph





Now draw a line through these points

So this is the graph of y=%281%2F2%29%2Ax-2 through the points (-8,-6) and (-6,-5)


So from the graph we can see that the slope is 1%2F2 (which tells us that in order to go from point to point we have to start at one point and go up 1 units and to the right 2 units to get to the next point) the y-intercept is (0,-2)and the x-intercept is (4,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=-2 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-2).


So we have one point (0,-2)






Now since the slope is 1%2F2, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-2), we can go up 1 units


and to the right 2 units to get to our next point



Now draw a line through those points to graph y=%281%2F2%29%2Ax-2


So this is the graph of y=%281%2F2%29%2Ax-2 through the points (0,-2) and (2,-1)