Answer:
The graph is given below.
Step-by-step explanation:
Given:
The inequality to graph is given as:
[tex]3x+4y>12[/tex]
In order to graph the above inequality, we first replace '>' sign by '=' sign and graph the line.
So, on replacing we get an equation of a line.
[tex]3x +4y=12[/tex]
Now, we find 2 points on the line to graph it.
Let x = 0, then
[tex]0+4y=12\\\\y=\frac{12}{4}=3[/tex]
So, the point is (0, 3).
Again, let y = 0, then
[tex]3x+0=12\\\\x=\frac{12}{3}=4[/tex]
So, another point is (4, 0).
Now, mark these two points on a graph.
Now, consider the inequality again in its original form.
The inequality sign is greater than (>). So, the line joining the two points is a broken line.
So, we draw a broken line passing through (0, 3) and (4, 0).
Now, since the left side of the inequality is greater than the right side, so the solution region is the part above the line as shown below.
