Complete the graph of 4x + y >= 4

[ndescandon]

Determine the correct half–plane in each case, and complete the graph.

4x + y ≥ 4

I have been trying to figure this one out don't seem to get it right so if someone can explain it to me i would be so grateful because than I can do the other 2 that I have to do
Thank you

 

[soroban]

Re: I need help!!!!!

Hello, ndescandon!

Determine the correct half–plane in each case, and complete the graph.
. . . \(\displaystyle 4x\,+\,y\:\geq\:4\)

First, graph the line: \(\displaystyle \:4x\,+\,y\:=\:4\)
. . It has intercepts: \(\displaystyle \,(1,\,0)\) and \(\displaystyle (0,\,4)\). .Draw the line.

Solve the inequality for \(\displaystyle y:\;\;y\:\geq\:-4x\,+\,4\)

Since the inequality is \(\displaystyle \geq\), shade the region above the line.

Because we have "greater than or equal to",
. . the answer includes the upper half-plane and the line itself.

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Another example: \(\displaystyle \:2x\,-\,y\:>\:6\)

Graph the line[, \(\displaystyle 2x\,-\,y\:=\:4\)
. . It has intercepts: \(\displaystyle (2,\,0)\) and \(\displaystyle (0,\,-6)\). .Draw the dotted line.

Solve for \(\displaystyle y:\;\;-y\:>\:-2x\,+\,4\)

Then we have: \(\displaystyle \:y\:<\:2x\,-\,4\)
[When multiplying or dividing by a negative, reverse the inequality.]

Since the inequality is \(\displaystyle <\), shade the region below the line.
. . The answer does not include the line; that's why we drew it "dotted".