Determine the type of boundary line and shading for the graph of the inequality 2x + y > 4.
Dashed line with shading on the side that includes the origin
Solid line with shading on the side that does not include the origin
Dashed line with shading on the side that does not include the origin
Solid line with shading on the side that includes the origin

Solution:

Given: Inequality is 2x + y > 4

The symbol here is > which indicates that the line of the graph will be dashed as it is not equal to.

Then you can solve for y by moving 2x to the other side and finding the two points on the graph

2x + y > 4

By subtracting 2x from both sides

2x + y - 2x > 4 - 2x

y > -2x + 4

Here the y-intercept is 4 (0,4)

Slope = -2 (down 2, right 1) (1, 2)

By connecting the two points we get the line above the origin

As y > -2x + 4, it should be shaded above and not included in the origin

Therefore, the type of boundary line and shading is a dashed line with shading on the side that does not include the origin.

Determine the type of boundary line and shading for the graph of the inequality 2x + y > 4.

Summary:

The type of boundary line and shading for the graph of the inequality 2x + y > 4 is a dashed line with shading on the side that does not include the origin.