Graphing a System of Linear Inequalities
Okay. I know to move ahead in any math course, you have to build a foundation in order to do so.
That said, it really peeves me when not only a professor during class lecture, or searching math help websites online, or the textbook don’t give clear step-by-step guiding on how to figure something out — such as, in the case I present in this post, hmm… how can I explain it… I guess, how to graph the damn inequality. No example I have seen yet shows this. I even looked in earlier sections in case I may have missed something I needed to know before tackling a more advanced problem.
Anyway, the problem presented is as follows:
Graph the solution of the system
- -2x + y ≤ -3
- x + 2y ≥ 4
So, as I was saying, I do understand dashed vs solid lines for these graphs, and finally, that “true” inequalities get shaded on the side of the line containing the test point and that “false” inequalities get shaded on the side of the line opposite the test point. Other than that, I’m lost. I get how to solve regular linear inequalities, but not how to graph on a coordinate plane.
Hopefully I haven’t lost anyone yet with all my babble or otherwise. I hope someone can point me in the right direction, either by leaving a comment here on this post with direct help or by leaving a comment with websites that can better explain this to me.
Thanks!
about 6 months ago
It sounds like you need help with graphing the lines. I don’t know what book you are using, but find a section on graphing lines. The way I tell my students to do this is solve the inequality for ‘y’. (The same way you would if there was an equal sign, just remember to flip the symbol if you divide/multiple by a negative on both sides.) So your two inequalities will look like this:
y ≤ 2x – 3
y ≥ (-1/2)x + 4
Now graph these two lines as if the had an equal sign (y=mx+b). “m” is the slope, and “b” is the y=intercept. Take the first inequality. Put a point at the y-interept of -3. Your slope is 2/1 (rise/run), so from the intercept count up two units and right one unit; put a second point and repeat from that point. Connect the points to draw your line. Do the same with the second inequality. This time your y-intercept is at positve 4, and your slope is (-1/2). This means from the intercept count down one and to the right two. Repeat and draw your line.
Now find your test point,(0,0), and shade accordingly. Hope this helps.
about 2 months ago
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Sent from my iPhone 4G
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