SOLUTION: graph the inequality: 4x+2y\le 8

Question 1202533: graph the inequality: 4x+2y\le 8
Found 2 solutions by Alan3354, math_tutor2020:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
graph the inequality: 4x+2y\le 8
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Makes no sense.
No inequality sign.
What does the \ backslash mean?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer:

Each "shade" refers to a shaded region. All of them are below the boundary.

Verbal description of the image shown above:
Draw the solid boundary line through (0,4) and (2,0)
Shade below the boundary.

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Further Explanation:

To graph we consider first the boundary line

What happens when x = 0?

We can then say the point (0,4) is on the boundary line. This is the y-intercept.

What about when y = 0?

The x-intercept is (2,0) where the line crosses the x axis.

Plot the two points (0,4) and (2,0).
Draw a straight line through them.
This forms the graph of 4x+2y = 8

Note: 4x+2y = 8 solves to y = -2x+4.

Now to determine which side we shade on.
Let's pick a test point.
(0,0) is the easiest in my opinion.
You can pick any point you like as long as it's NOT on the boundary.

We arrive at a true statement at the end, which makes also true when (x,y) = (0,0).

We'll shade the entire side that contains (0,0)
Meaning we shade below the boundary.

In other words, shade each sub-region labeled "shade".
All of which are below the solid boundary line.

The boundary line is solid because of the "or equal to".
Points on the boundary -- such as (1,2) -- are in the shaded solution set.

You can use a tool like Desmos and GeoGebra to verify the answer.

Desmos graph
https://www.desmos.com/calculator/nvlqxtihsi

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