graph the inequality

Question

y < 4x + 2
select the option for the boundary line:
a solid line
b dashed line
turn on the shading option and move the black point to show where to shade the half-plane:
a turn off shading
b turn on shading

Answer 1

To graph the inequality \(y < 4x + 2\):

1. Identify the Boundary Line: The equation \(y = 4x + 2\) represents a straight line. Since the inequality is "less than" (not "less than or equal to"), the boundary line should be a dashed line to indicate that points on the line are not included in the solution.

   • Select option: b dashed line.

2. Shading the Appropriate Half-Plane: The inequality \(y < 4x + 2\) indicates that we are interested in the region below the line (where the y-values are less than those on the line). Thus, the shading should be turned on to represent the area where the inequality holds true.

   • Select option: b turn on shading.

So, the final actions to take are:

• Use a dashed line for the boundary.
• Turn on shading to indicate the solution area that satisfies \(y < 4x + 2\).