Question

Which is the graph of 4x-8y<=9

Answer 1

Given inequality is
`4x-8y\le9`

Now we need to find the graph of
`4x-8y\le9`.

Which can be done into two parts:

First graph the line
`4x-8y=9` then shade the graph for inequality sign
`\le`

Graph the line
`4x-8y=9`

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

`y=(9)/(-8)`

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

`x=(9)/(4)`

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
`\le` 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.

`4x-8y\le9`

`4*0-8*0\le9`

`0-0\le9`

`0\le9`

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: