Graph the solution set for the linear inequalities.

y<4x+2
2x−y≥2

draw a dotted line y = 4x+2, (your line is to be excluded)

and shade in the region below the line

2x - y ≥ 2
-y ≥ -2x + 2
y ≤ 2x - 2
draw a solid line y = 2x-2, and shade in the regions below it
your solution is the intersection of the 2 regions

To graph the solution set for the linear inequalities, we will first graph the boundary lines for each inequality and then determine the shaded regions that represent the solution set.

For the first inequality, y < 4x + 2, we start by graphing the boundary line y = 4x + 2. To do this, we need to find two points on the line. One way to find these points is by setting x = 0 and solving for y, and setting y = 0 and solving for x.

Setting x = 0:
y = 4(0) + 2
y = 2

Setting y = 0:
0 = 4x + 2
4x = -2
x = -1/2

So, we have two points: (0, 2) and (-1/2, 0).

Plotting these points on a coordinate plane, we draw a line through them to represent the boundary line. Note that the line is dashed because the inequality is strict (y < 4x + 2).

Next, for the inequality 2x - y ≥ 2, we graph the boundary line 2x - y = 2. Again, finding two points on the line:

Setting x = 0:
2(0) - y = 2
y = -2

Setting y = 0:
2x - 0 = 2
2x = 2
x = 1

So, we have two points: (0, -2) and (1, 0).

Plotting these points on the same coordinate plane, we draw a line through them to represent the boundary line. Note that the line is solid because the inequality is not strict (2x - y ≥ 2).

Now, we determine the shaded region that represents the solution set. Since the first inequality is y < 4x + 2, the region below the dashed line represents the solution set for it. And since the second inequality is 2x - y ≥ 2, the region above the solid line represents the solution set for it.

Shade the regions accordingly, and the solution set is the overlapping region between the two shaded regions.

I hope this explanation helps you understand how to graph the solution set for linear inequalities.