Answer:
Given Inequalities are,
[tex]y>\frac{1}{4}x+6[/tex]
[tex]y>2x-1[/tex]
We need to graph the in equality.
First we find the point to draw the lines of the inequality.
By taking them equal we find point.
Consider,
[tex]y=\frac{1}{4}x+6[/tex]
put, x = 0 ⇒ y = 6
put x = 4 ⇒ y = 1 + 6 = 7
So point to draw first line ( 0 , 6 ) and ( 4 , 7 )
Now Consider,
y = 2x - 1
put , x = 0 ⇒ y = -1
put , x = 4 ⇒ y = 8 - 1 = 7
So Points of the second line is ( 0 , -1 ) and ( 4 , 7 )
Since, the inequalities are strict then in graph lines drawn is dotted line as point on line does not includes in the inequality.
For Inequality put ( 0 , 0 )
[tex]y>\frac{1}{4}x+6[/tex]
[tex]0>6[/tex]
origin does not satisfy it. So, Region we shade is opposite to side in which origin belong.
[tex]y>2x-1[/tex]
[tex]0>-1[/tex]
origin does satisfy it. So, Region we shade is to side in which origin belong.
Therefore, The graph we get is attached.
