Answer:
Given inequality:
[tex]y>3x-4[/tex]
To graph it.
Solution:
In order to graph the given inequality, we will first graph the equation of the line by replacing the inequality sign with equal to sign.
Thus, we will graph the line [tex]y=3x-4[/tex]
On comparing the line equation with standard equation [tex]y=mx+b[/tex] where [tex](0,b)[/tex] represents the y-intercept point of the line, we can conclude the y-intercept point for the given line is [tex](0,-4)[/tex]
We can find another point by plugging in [tex]x=1[/tex] in the equation.
So, we have:
[tex]y=3(1)-4[/tex]
[tex]y=3-4[/tex]
[tex]y=-1[/tex]
So, the other point is [tex](1,-1)[/tex]
Potting (0,-4) and (1,-1) on the graph.
We can joint the two points and extend it infinity in order to graph the equation of line.
Now, since the inequality sign is greater than,
1) so we make sure that the line of the equation is a broken line as the line is not included in the solution for the inequality.
2) The part of the graph lying above the line would be shaded as the solution for the inequality.
