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.

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

Step-by-step explanation:

we have

[tex]2y > x-2[/tex]

The solution of the inequality is the shaded area above the dashed line

The equation of the dashed line is [tex]2y=x-2[/tex]

The slope of the dashed line is positive

The y-intercept of the dashed line is (0,-1)

The x-intercept of the dashed line is (2,0)

therefore

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

see the attached figure to better understand the problem

pinquancaro pinquancaro · Answer 2 · 2019-10-02T10:35:33+02:00

Answer:

Option 3

Step-by-step explanation:

Given : Linear inequality [tex]2y>x-2[/tex]

To find : Which is the graph of linear inequality ?

Solution :

Linear inequality [tex]2y>x-2[/tex]

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

The linear equation is [tex]2y=x-2[/tex]

The general slope form of line is [tex]y=mx+c[/tex]

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

Re-write the equation [tex]y=\frac{1}{2}x-1[/tex]

On compare,

Slope is positive [tex]m=\frac{1}{2}[/tex]

The y-coordinate is (0,-1)

For x-coordinate put y=0,

[tex]2(0)=x-2[/tex]

[tex]x=2[/tex]

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.