How do you graph #3x-4y \ge 12#?

1 Answer
KillerBunny
Jan 21, 2015

You can manipulate the expression until it looks like something very easy to figure out:

  • First of all, add #4y# on both sides, and get #3x \geq 12+4y#
  • Secondly, subtract 12 from both sides, and get #3x-12 \geq 4y#
  • Lastly, divide both sides by 4, and get #\frac{3}{4}x -3 \geq y#

You obviously can read this last inequality as
#y \leq \frac{3}{4}x -3#. We know that if the equality holds, #y= \frac{3}{4}x -3# represents a line, thus the inequality represents all the area below (since we have that #y# must be lesser or equal than the expression of the line) that said line. graph{y <= 3/4x -3 [-18.13, 21.87, -12.16, 7.84]} This is the graph, where you can see the line #y= \frac{3}{4}x -3# in a darker blue, while the lighter-blue painted area is the one where #y < \frac{3}{4}x -3# holds.

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