How would I solve this linear inequality and graph it?
3x-y

Question

How would I solve this linear inequality and graph it?
3x-y<4

e.mccormick · Answer

Solve it for y.  Then it is pretty similar to graphing a line.  But you also end up with a shaded area.

anonymous · Answer

You'd put it as y=-3x+4, correct? That's about as far as I've gotten

e.mccormick · Answer

ummm.... how did your, ah.  You dropped the - on the y and forgot about it.

anonymous · Answer

That's why I'm asking for help. I don't really know what I'm doing

e.mccormick · Answer

Well, what you really have at this point is:
$-y<-3x+4$

If you divide out the -, or -1, what happens to that?

anonymous · Answer

y<3x-4?

e.mccormick · Answer

Very, very close!  When you divide/multiply a negative in an inequality, the arrow changes!  $< \rightarrow >$

e.mccormick · Answer

So: $y>3x-4$  c:

Do you get that part?

anonymous · Answer

yup so what would be the next step?

e.mccormick · Answer

As an example:
$5>-1$
$(-1)(5>-1)$
$-5<1$



OK, so next, you need to find that line.  Now,there is a clue as to if a line is part of the graph, or if it is dashed.... or are you doing these on number lines?  On a number line it is an open circle or a closed one.

anonymous · Answer

I think that < is just a dashed line but if it was greater/less than or equal to it would be solid. Or is it the other way around?

e.mccormick · Answer

You got it!

$=$, $\le$, and $\ge$ are solid lines and part of the graphed value.

$\ne$, $<$, and $>$ are dashed lines and the border next to the graphed value.

e.mccormick · Answer

OK, now, you goow with the graphing the line part?

e.mccormick · Answer

good...

anonymous · Answer

I don't know what I'm supposed to plug in, in order to get the points

e.mccormick · Answer

0 is easy.  Put 0 in for y and get the x intercept.  Then put in 0 for x and get the y intercept.

anonymous · Answer

and those are the only points I'd need?

e.mccormick · Answer

Any two points determine a line.  Graph them and you can draw a dashed line through them.  Line part done and all that is left is shading!

e.mccormick · Answer

For the shading:

$y \le stuff$ and $y < stuff$  mean the y values are valid below the line.

$y\ge stuff$ and $y> stuff$ mean the y values are valid above the line.



On a side note, why I picked 0:

The two most important numbers in doing math problems: 0 and 1.  ($e\text{ and } \pi$ are great, but 0 and 1 rule!)  

See, $x+0 = x+a-a$ which comes in handy for completing the square.  

$\dfrac{x}{n}=\dfrac{x}{n}\times \dfrac{a}{a}=\dfrac{xa}{an}$ which is just multiply by 1 and comes in handy for tons of things!

e.mccormick · Answer

Did your points come out something like this?
|dw:1380088243260:dw|

anonymous · Answer

Yeah they came out that way and I shaded above where the line would be and got the problem right :) thank you so much for taking the time to explain things to me

e.mccormick · Answer

So this: https://www.desmos.com/calculator/2vme81vjwq Good! have fun!