# Thread: How do i know where to graph this linear inequality in 2 variables?

1. ## How do i know where to graph this linear inequality in 2 variables?

X+2y greater than or equal to -3

I am having trouble figureing out how to graph it. How does -3 get graphed when it dosent have an x or y to it?

2. ## Re: How do i know where to graph this linear inequality in 2 variables?

Originally Posted by cytotoxictcell
X+2y greater than or equal to -3

I am having trouble figureing out how to graph it. How does -3 get graphed when it dosent have an x or y to it?
\displaystyle \displaystyle \begin{align*} x + 2y &\geq -3 \\ 2y &\geq -x - 3 \\ y &\geq -\frac{1}{2}x - \frac{3}{2} \end{align*}

So you will need to graph the line $\displaystyle \displaystyle y = -\frac{1}{2}x - \frac{3}{2}$ and accept everything that's above that line (in other words, shade everything below it...)

3. ## Re: How do i know where to graph this linear inequality in 2 variables?

Ok i am really confused now.
I simply solved the problem by finding the y+x Intercepts =(. What am i suppose to?

4. ## Re: How do i know where to graph this linear inequality in 2 variables?

Originally Posted by cytotoxictcell
Ok i am really confused now.
I simply solved the problem by finding the y+x Intercepts =(. What am i suppose to?
Do you know how to graph the line $\displaystyle x+2y=-3~?$
If so, draw that graph.
See on which side of the line points satisfy the inequality.

If you do not know that, then stop, go back, and learn to graph an equation of a line.

5. ## Re: How do i know where to graph this linear inequality in 2 variables?

Originally Posted by cytotoxictcell
X+2y greater than or equal to -3

I am having trouble figureing out how to graph it. How does -3 get graphed when it dosent have an x or y to it?
Your mistake is thinking that the number -3 gets graphed at all! First graph the equation x+ 2y= -3. Then determine which side is is ">" and which side is "<".

6. ## Re: How do i know where to graph this linear inequality in 2 variables?

Originally Posted by cytotoxictcell
Ok i am really confused now.
I simply solved the problem by finding the y+x Intercepts =(. What am i suppose to?
Obtaining the intercepts was ok too.
Following on from all the good posts above and in response to your 2nd posting....

When $\displaystyle x=0\Rightarrow\ y\ge\ -\frac{3}{2}$

When $\displaystyle y=0\Rightarrow\ x\ge\ -3$

Now if you draw the line through the intercepts, you have the line representing $\displaystyle x+2y=-3$

If you wish, you may test the point (0,0) to see whether it is in the

$\displaystyle x+2y\ge\ -3$

or

$\displaystyle x+2y\le\ -3$

region.