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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
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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.
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Plot: (0,4) and (1,2) and draw a dashed line thru them
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Since you want y LESS than the boundary, shade
the half-plane BELOW the boundary to get the graph
of the inequality:
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2.) Graph 4x - 3y >= 12
Solve for "y":
3y <= 4x-12
y <= (4x-12)/3
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Now graph the boundary as a solid
line because it is part of the problem
Plot (0,-4)(2,-4/3)
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Shade the half-plane BELOW the boundary
because you want y LESS than the boundary.
The line and the shaded area are the graph.
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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
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