Expert: Socrates - 7/27/2005

Question
What does the inequality 2x-4y<-6 look like on a graph? Where is it shaded? above or below the line?  
What if the equation stays the same, but the <,> changes and now has a line underneath it. Then what would it look like?
See, i'm looking for one of these equations to look like my paper, and i cant figure it out. My graph on my paper is shaded above the line, and it crosses the x-axis at (-3,0), and the y-axis at (0,1 1/2)
Could you help me with this? do you understand what i mean? Thank you soso much~!

Answer
I think the easiest way to understand this is to first solve the inequality for y.

2x - 4y < -6

4y > 2x + 6

y > (1/2)x + 3/2

Since we see that y must be greater, the points that satisfy the inequality lie above the line y = (1/2)x + 3/2.
So you you shade the points above the line. Just the points above the line, but not on the line, because y is greater than , but not equal. By the way , you have correctly identified the x and y intercepts, so your line is correct!

If the "<" changed to "< or =" , you solve for y in the same way and get

y < or =  (1/2)x + 3/2

Since y must now be less than, we shade below the line
y = (1/2)x + 3/2

In this case , you also include points actually on the line because "=" is allowed.

To avoid confusion in these problems , always solve the inequality for y first.