SOLUTION: Hello. I am having such a hard time understanding how to graph linear inequalities, from solving the problem to understanding where the points go on the x and y axis, if the line s

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Question 405570: Hello. I am having such a hard time understanding how to graph linear inequalities, from solving the problem to understanding where the points go on the x and y axis, if the line should be solid or dashed. I just can't make it click in my brain. Can you possibly show a very blunt breakdown of the following two equations? If I can follow it step by step I should be able to get it. Thank you so much!
1.) Graph 2x + y < 4
2.) Graph 4x - 3y >= 12
Found 2 solutions by stanbon, ewatrrr:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
1.) Graph 2x + y < 4
Solve for "y":
y < -2x+4
----
You NEVER graph an inequality directly.
You graph its boundary which is always an equality.
Graph y = -2x+4 as a dashed line because equality
is not part of your problem.
---
Plot: (0,4) and (1,2) and draw a dashed line thru them
----
Since you want y LESS than the boundary, shade
the half-plane BELOW the boundary to get the graph
of the inequality:

====================
2.) Graph 4x - 3y >= 12
Solve for "y":
3y <= 4x-12
y <= (4x-12)/3
---
Now graph the boundary as a solid
line because it is part of the problem
Plot (0,-4)(2,-4/3)
---
Shade the half-plane BELOW the boundary
because you want y LESS than the boundary.
The line and the shaded area are the graph.

=============================================
Cheers,
Stan H.
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!


Hi

2x + y < 4   OR y < -2x + 4

I.  Graph line y = -2x + 4 by plotting points a couple of points(0,4) and (1,2)

for ex and connect with a 'dotted line' due to the < sign. (cannot demonstate that here)



II.  Shade below the dotted line to show the graph of the Inequality 




 
Solved by pluggable solver: Plot Any Inequality


Graphing function : 

  

  



 

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