Question

Which is the graph of linear inequality 2y > x – 2?

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the right of the line is shaded.

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the right of the line is shaded.

Answer 1

Option 3

Explanation:

Given : Linear inequality
`2y>x-2`

To find : Which is the graph of linear inequality ?

Solution :

Linear inequality
`2y>x-2`

First we figure out the slopes and coordinates through which it pass.

The linear equation is
`2y=x-2`

The general slope form of line is
`y=mx+c`

Where, m is the slope and c is the y-coordinate

Re-write the equation
`y=(1)/(2)x-1`

On compare,

Slope is positive
`m=(1)/(2)`

The y-coordinate is (0,-1)

For x-coordinate put y=0,

`2(0)=x-2`

`x=2`

The x-coordinate is (2,0).

Now, Plotting the linear inequality and mark the point (-4,-3).

Refer the attached figure below.

We get, On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.

Therefore, Option 3 is correct.