Given inequality is [tex]4x-8y\le9[/tex]
Now we need to find the graph of [tex]4x-8y\le9[/tex].
Which can be done into two parts:
First graph the line [tex]4x-8y=9[/tex] then shade the graph for inequality sign [tex]\le[/tex]
Graph the line [tex]4x-8y=9[/tex]
we can plug any number for x say x=0 to find the y-value
4x-8y=9
4*0-8y=9
0-8y=9
-8y=9
[tex]y=\frac{9}{-8}[/tex]
y=-1.125
Hence first point is (0,-1.125)
Similarly we can plug y=0 then solve for x
4x-8y=9
4x-8*0=9
4x-0=9
4x=9
[tex]x=\frac{9}{4}[/tex]
x=2.25
hence 2nd point is at (2.25,0)
Now graph both points and join them by a straight line.
Since used inequality is [tex]\le[/tex] so we use solid line not the dotted line.
Shading the graph:
we can pick any test point which is not on the line 4x-8y=9 say (0,0) then plug into original problem to see if that point satisfies the original problem or not.
[tex]4x-8y\le9[/tex]
[tex]4*0-8*0\le9[/tex]
[tex]0-0\le9[/tex]
[tex]0\le9[/tex]
Which is TRUE.
TRUE means shade in direction of test point otherwise we graph in opposite direction of test point.
Now final graph will look like the graph attached below:
