Question

Which is the graph of linear inequality 2x-3y<12 ?

Answer 1

Option 3

Explanation:

Given : Inequality
`2x-3y<12`

To find : Which is the graph of linear inequality ?

Solution :

Inequality
`2x-3y<12`

Solve for y,

`2x-12 < 3y`

`y>(2)/(3) x-4`

Now, We plot the graph of the equation using x-intercept and y-intercept,

x-intercept is when y=0,

`(2)/(3) x-4=0`

`(2)/(3) x=4`

`x=6`

y-intercept is when x=0,

`(2)/(3)(0)-4=y`

`y=-4`

So, Graph passing through (0,-4) and (6,0).

Now, The area of the graph is

Put x=0 and y=0

`2(0)-3(0)<12`

`0<12`

It is true. So, The region is towards origin.

The inequality is not have equal sign so the line is dotted.

From the given graph Option 3 is correct.

Refer the attached figure below.