SOLUTION: How do you turn this inequality into an equation you can graph 9x-2y<-18?

Question 206056: How do you turn this inequality into an equation you can graph 9x-2y<-18?
Found 2 solutions by RAY100, stanbon:
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Let's make a base line by assuming 9x-2y = -18
.
The T box might look like
.
x,,,,,,,,,,,,y
.
0,,,,,,,,,,,,9,,,,,,,-2y=-18
.
-2,,,,,,,,,,,0,,,,,,,,9x= -18
.
2,,,,,,,,,,,18,,,,,,,,9x-36 =-18
.
Now, plot these using a dashed line, no equal sign,
.
Now, ,lets pick which side of the line of the "area of concern.
.
The test point might be (0,0),,,below the line,,,,,
our eqn becomes, 9(0)-2(0) < -18,,or 0<-18, which is NOT TRUE,,,,
therefore our answer is above the line.
.
To verify, lets pick a point above the line, (0,10) and see if the eqn is valid,,,,,,9(0) -2(10) < -18,,,,-20<-18,,,ok, so area is above line.
.
Usually we shade this area by cross hatching.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How do you turn this inequality into an equation you can graph 9x-2y<-18?
---------------------
You graph the boundary of the inequality, which is the equality.
---
Solve the inequality for "y":
2y < 9x + 18
y < (9/2)x + 2
------------------------
Graph the boundary which is y = (9/2)x + 2
-----------------------------------------------

--------------------
Now look at the inequality.
Since you want y to be LESS than the boundary,
shade the half-plane BELOW the boundary.
That shaded half-plane is the graph of the inequality.
====================================================
Cheers,
Stan H.
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