How do you graph 3x-4y \ge 123x−4y≥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 4y4y on both sides, and get 3x \geq 12+4y3x≥12+4y
  • Secondly, subtract 12 from both sides, and get 3x-12 \geq 4y3x−12≥4y
  • Lastly, divide both sides by 4, and get \frac{3}{4}x -3 \geq y34x−3≥y

You obviously can read this last inequality as
y \leq \frac{3}{4}x -3y≤34x−3. We know that if the equality holds, y= \frac{3}{4}x -3y=34x−3 represents a line, thus the inequality represents all the area below (since we have that yy 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 -3y=34x−3 in a darker blue, while the lighter-blue painted area is the one where y < \frac{3}{4}x -3y<34x−3 holds.

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