What exactly is the boundry line? What does it mean by 'above or below the origin'
"What does it mean by, "The origin."?
Determine the type of boundary line and shading for the graph of the inequality y > 2x + 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."
"What does it mean by, "The origin."?
Determine the type of boundary line and shading for the graph of the inequality y > 2x + 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."
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A single inequality divides the xy-plane into two regions. In one of the regions, there is no point that satisfies the inequality, and in the other region every point satisfies the inequality. When the inequality is "strict" ("<" or ">") the boundary is dashed; when it is not "strict" ("≤" or "≥") the boundary is solid.
In most cases (including yours), the inequality is a linear inequality. Then its boundary is a line (dashed or solid depending on the inequality). In your case, the boundary line is y = 2x + 6, and it should be drawn as a dashed line.
"The origin" is where the x- and y-axes intersect. It has coordinates (0, 0).
Conventionally, the positive x-axis points to the right, and the positive y-axis points up, When you plot the boundary y = 2x + 6 (dashed), you will see that this line is above the origin,
Now, you need to decide which piece of the xy-plane is the solution to the inequality. To do this, choose any point not on the line y = 2x + 6 and insert its coordinates into the inequality. If the result is a true statement, then the piece from which you chose the point is the solution (which you should shade). The choices given indicate that you should check the origin (i.e., x = 0, y = 0):
0 > 2(0) + 6
0 > 6
Is this a true statement? No, it's not. Therefore, the side to be shaded is the one that does not include the chosen point (here, the origin).
In most cases (including yours), the inequality is a linear inequality. Then its boundary is a line (dashed or solid depending on the inequality). In your case, the boundary line is y = 2x + 6, and it should be drawn as a dashed line.
"The origin" is where the x- and y-axes intersect. It has coordinates (0, 0).
Conventionally, the positive x-axis points to the right, and the positive y-axis points up, When you plot the boundary y = 2x + 6 (dashed), you will see that this line is above the origin,
Now, you need to decide which piece of the xy-plane is the solution to the inequality. To do this, choose any point not on the line y = 2x + 6 and insert its coordinates into the inequality. If the result is a true statement, then the piece from which you chose the point is the solution (which you should shade). The choices given indicate that you should check the origin (i.e., x = 0, y = 0):
0 > 2(0) + 6
0 > 6
Is this a true statement? No, it's not. Therefore, the side to be shaded is the one that does not include the chosen point (here, the origin).