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".