Question 203050: How to graph 4x+y>=4
Answer by PRMath(133)   (Show Source):
You can put this solution on YOUR website! How to graph 4x+y>=4
To graph this, you will have to first find your "X" and "Y" intercepts.
To find your y intercept, solve for y by making x = 0.
To find your x intercept, solve for x by making y = 0.
So let's look at your equation and pretend it is not a greater than problem. Let's just pretend it is an "=" problem.
4x+ y = 4 Now let's solve for the y intercept by making x = 0
4(0) + y = 4 (See how I plugged "0" in for the "X"?
0 + y = 4 (4 times 0 is 0)
y = 4
In other words, when x = 0, then y = 4. Therefore, your y intercept would be listed as: (0, 4)
Now let's find the "X" intercept.
4x + y = 4 Solve for the x by making y = 0
4x + 0 = 4 (see how I plugged 0 in for "Y"?)
4x = 4
 =  (Divide both sides by 4 to isolate the "Y")
x = 1
In other words, when y = 0, then x = 1. Therefore, your x intercept would be listed as: (1, 0)
Now you know two points on the coordinate plane. Those points are:
(1, 0) and (0, 4). If you plot those points and the connect the dots, you will have your line.
HOWEVER --- let's go back and look at this original equation......
4x + y > =4
(Since you are listing this with a greater than sign AND an equal sign, I am supposing you want to indicate that this is a greater than/or equal to equation, yes? If you meant to make your 4 a NEGATIVE 4, then you will have a different answer, (and I will give you that answer below) but I'll go with the idea that you meant a POSITIVE 4 and a greater than or equal to equation, k?)
Sooooo your equation is:
4x + y > =4
You have connected the dots and because this is a greater than or equal to equation, you can connect the dots with a SOLID line. If this had been just a greater than problem or just a less than problem (without an "equal to" part of the equation) your line would be dotted.
Now you have to decide where you should shade the line. To determine shading, you can just choose (0, 0) to work with and by that I mean, choose the point (0, 0) and plug that into your original equation, like this:
4x + y > =4
4(0) + 0 >= 4
0 + 0 >=4
0>= 4
See how I plugged in 0 for the "x" in the equation and 0 for the "y" of the equation? I ended up with the equation: 0 >= 4. Is it true that 0 is >= to 4??? NOOOO it is not! Zero is LESS than 4. Therefore, do NOT shade in the area where the point (0, 0) is! Instead, you should shade on the OTHER side of the line, away from the (0, 0) point.
Now... JUST IN CASE you meant your equation as 4x+y>-4 (see the NEGATIVE 4?) I will do the work, but without any explanation, k? The explanation will be the same as above, but with different answers. Here goes:
Y INTERCEPT
4x+y = -4
4(0) + y =-4
y = -4
Y intercept: (0, -4)
X INTERCEPT
4x+y = -4
4x + 0 = -4
4x = -4
x = -1
X intercept (-1, 0)
Plot X and Y Intercepts on a coordinate plane and connect the dots with a DOTTED LINE.
Now for shading.......Choose to plug in the points (0, 0)
4x+y > -4
4(0) + 0 > -4
0 > -4
Is this true? YES! Therefore, shade in the area to the right of this line so that the point (0, 0) is included in the shaded area.
I hope this helps. :-)
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