How do you graph the inequality –3x – 4y<=12?

1 Answer
KillerBunny
Feb 5, 2015

To graph this kind of inequality, the best thing is to manipulate them and obtain a relation of the form y\le f(x) (or y \ge f(x)).

In fact, we know that y=f(x) is exactly the graph of f, and so y\le f(x) (or y \ge f(x)) represents all the portion of the plan below (or above) the graph of f.

Let's do those manipulations: starting from
-3x-4y\le 12,
adding 4y at both sides we get
-3x \le 4y+12.
Subtracting 12 at both sides, we have
-3x-12\le 4y.
Dividing both sides by 4 we finally have
-3/4 x - 3 \le y
which can of course be read as
y \ge -3/4 x - 3

We thus have f(x)=-3/4 x - 3, which is a line and so it's very easy to graph. Once graphed, you need to consider all the portion of plan above the line to solve your inequality.

Here's the graph: graph{-3x-4y \le 12 [-10, 10, -5, 5]}

Related questions
See all questions in Linear Inequalities in Two Variables
Impact of this question
8437 views around the world
You can reuse this answer
Creative Commons License