Answer:
4). [tex]y<\frac{1}{2}x-4[/tex] (look at my explanation for how to graph)
5.) [tex]y<\frac{?}{?}x+?[/tex] (look at my explanation for how to get the correct numbers)
6.) [tex]x\geq 2[/tex] (look at my explanation for how to graph)
Step-by-step explanation:
Question 4:
Solving for y:
First it's better if you solve for y then graph, it's easier that way.
[tex]x-2y>8\\-2y>-x+8\\y<\frac{1}{2}x-4[/tex]
As you might notice the greater than sign flipped, that doesn't always happen. It only happens when you are dividing by a negative number.
Graphing the inequality:
When you start graphing you should always start by plotting the y-intercept. Which in this case it's [tex](0,-4)[/tex]. Then starting from that point you would go up 1 unit then right 2 units then plot the new point because the slope is [tex]\frac{1}{2}[/tex]. The 1 would be the up and down as for the 2 it will be the right and left. This goes up 1 and right 2 because it's positive. So you keep going creating new points as you go then when you reached the end of the graph you would go back to [tex](0,-4)[/tex] and do the opposite so you will do down 1 then left 2. When you run out of room you will have to draw a line, but be careful the line has to be dotted because the solid lines are used for the greater/less than or equal to signs. Then make sure to add arrows at each side of the dotted line to indicate that this line is infinite.
Question 5:
I'm very sorry but I can't see the picture since it's a bit blurry. So I'll try to explain how to write the inequality the best I can. So first we need to know the y-intercept it should be the point directly on the y-axis. Then find the slope by seeing how it gets to the next perfect point. I can tell you that the slope will be positive. Also for the sign it's dotted that means the sign is [tex]<[/tex]. So the inequality should look something like this [tex]y<\frac{?}{?}x+?[/tex]. Make sure you have the signs correct too don't change the ones I already put in.
Question 6:
For this one the inequality will look like this [tex]x\geq 2[/tex]. Then for the graph you will plot [tex](2,0)[/tex]. Then make a solid line that goes vertically since the only x-value is 3 the y-value will be changing without the x. Then for the shading you will shade the right side of the line.
