Question 201954: Help Needed;
Graph the linear inequality.
2x + 4y ≤ 8
Answer by PRMath(133)   (Show Source):
You can put this solution on YOUR website! Help Needed;
Graph the linear inequality.
2x + 4y ≤ 8
Here's an easy way to do this work:
First, these two hints are good to know:
To find the y intercept, solve for Y by making x = 0
To find the x intercept, solve for X by making y = 0
Ok then, let's proceed......
Here's your equation: 2x + 4y ≤ 8
Let's just solve this as if there were an = sign in the equation.
AND, let's solve this for first for our y intercept and then the x intercept.
y intercept - solve for y by making x = 0
2x +4y= 8
2(0) + 4y = 8
0 + 4y = 8
y = 2
y intercept: (0, 2)
x intercept - solve for x by making y = 0
2x + 4y = 8
2x + 4(0) = 8
2x = 8
x = 4
x intercept: (4, 0)
Now we have two points that we can plot on a coordinate plane and thennnn when you connect the dots, you'll have your line.
BUT we are not done. We have to decide which side to shade. The way to shade is easy.....
Do you see that the point (0.0) is on one side of the line you just drew?
Let's "plug" (0, 0) into the original equation:
2x + 4y ≤ 8
2(0) + 4(0) ≤ 8
0 + 0 ≤ 8
0 ≤8
Is 0 less than or equal to 8? If the answer is YES (and the answer is indeed yes) then you just shade the side of the line that made that statement true. In other words, shade in the side that held the ordered pair of (0,0), because (0,0) made your original statement true.
I hope this helps. :-)
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