Question

How do you graph $y \geqslant - 3x + 4$?

Answer 1

Hint: In this question, the linear equation in two variables is given. Any linear equation in two variables can be represented in the form of $ax + by + c = 0$. Where a, b, and c are real numbers and ‘a’ and ‘b’ are not equal to 0. We will first treat it as equality and find the equation of the line by plotting any two points on it. Now, we will just shade the region accordingly and get the required region.

Complete step-by-step solution:
In this question, we want to graph the inequality $y \geqslant - 3x + 4$.
Instead of treating it as an inequality, let us for once remove it as less than sign and treat it as an inequality.
So, now we need to graph $y = - 3x + 4$.
Now, let us find two points on this line and thus join them to form the above line.
First, let us put x is equal to 0 in the above equation.
 $ \Rightarrow y = - 3x + 4$
Put x=0.
$ \Rightarrow y = - 3\left( 0 \right) + 4$
So,
$ \Rightarrow y = 4$
Now, let us put x is equal to 1 in the above equation.
 $ \Rightarrow y = - 3x + 4$
Put x=1.
$ \Rightarrow y = - 3\left( 1 \right) + 4$
That is equal to,
$ \Rightarrow y = - 3 + 4$
So,
$ \Rightarrow y = 1$
Hence, we get the following table.

X	0	1
Y	4	1

Now, we have the inequality of greater than, therefore, the shading will be outside.
Now, let us plot this line.

Note: We first treated the given inequality as equality because we first needed to find the boundary line of the graph and after finding the boundary line; we just see where the graph intends to be. To check whether we have to shade inwards towards the origin or outwards, you should just put the origin in the given inequality and if we get the correct result, we shade inwards, otherwise outwards.