Question

Determine the type of boundary line and shading for the graph of the inequality -3x + y > 6.

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.

Answer 1

@mathstudent55

Answer 2

To plot an inequality, start out by plotting the corresponding equation.
All that means is replace the inequality sign by an equal sign.
For 3x + y > 6, plot 3x + y = 6.
If you have, in the inequality, \(>\) or \(<\), use a dashed line.
If you have, in the inequality, \(\ge\) or \(\le\), use a solid line.

Answer 3

That's the first step.
The second step is to determine which side of the line is shaded.

Answer 4

Ok

Answer 5

please too provide me the correct option.

Answer 6

To do that, pick a point not on the line, usually the origin (0, 0) is easy, and substitute into the original inequality. If the point makes the inequality true, then every point on the same side as the point you picked is true and that side of the line is shaded. If the point does not make the inequality true, then shade the other side.

Answer 7

then what can be the correct option ?

Answer 8

Here you can just answer the questions:
1. Is the line solid or dahsed? Since all we have is >, the line is dashed.
2. Does the origin, (0, 0) work?
3x + y > 6
3(0) + 0 > 6
0 + 0 > 6
0 > 6 is false, so side containing origin is not shaded. The side not containing the origin is shaded.