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Question 160852: I would try to answer the problem but I really don't know where to begin. Can you please help me with the following problem?
Graph the solution set of 3x-4y>8.
Thank You for your help!
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! to graph the equation, you need to put it into the form of y < f(x).
in order to do that you want to get the y on the left side of the equation and you want to get the x and everything else on the right side of the equation.
your equation starts as 3*x - 4*y > 8
subtract 3*x from both sides of the equation to get
-4*y > 8 - 3*x
divide both sides of the equation by 4*y to get
-y > (8 - 3*x)/4
if you want to make y positive, you need to multiply both sides of the equation by (-1).
if you do that, the inequality reverses, and you get
y < (-1) * (8-3*x)/4 which becomes
y < (-8+3*x)/4 which becomes
y < (3*x-8)/4
to graph this equation, you need to graph the equality.
you take y = (3*x-8)/4 and graphs it.
it looks like this
scan below the graph for further comments
since that graph is y = (3*x-8)/4, if you want y < (3*x-8)/4, then you want every value of y that is less than the value of y shown on that line.
this becomes the area under the line in the graph created by the equation of y = (3*x-8)/4.
on your graph (i can't do it here), you would shade the area under the graph and that would be your solution.
to test, you would take any value of x.
let's say x = 8.
solve the equation for y = (3*x-8)/4 when x = 8
the equation becomes y = (3*8 - 8)/4 = 2*8 / 4 = 8/2 = 4
so when x = 8, y = 4
any value of y < 4 will satisfy the equation y < (3*8-8)/4.
all those values of y will be in the area under the line.
this holds true for all values of x.
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