SOLUTION: I just dont get how to graph inequality. Graph the inequality x< -3y -

Question 421517: I just dont get how to graph inequality.
Graph the inequality x< -3y
-
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
to graph any equation, you need to solve for y.

then you need to graph the equality.

then you need to determine the area of the inequality.

your equation is x < -3y

add 3y to both sides of the equation and subtract x from both sides of the equation to get:

3y < -x

divide both sides of the equation by 3 to get:

y < -x/3

that's your inequality after you solved for y.

now graph the equality.

the equality is y = -x/3

this is what you graph.

your graph will look like this:

when you look at this graph, you see that the line is all points where y = -x/3.

now look at your inequality equation.

that is y < -x/3

in order for the value of y to be smaller than -x/3 for any value of x, you will need to be in the area of the graph that is beneath the line.

you would shade that area to indicate that the solution to the equation of y < -x/3 is in that area.

for example:

when x = 3, the value of the equation of the line y = -x/3 becomes -1.

you can see that the value of y = -1 when x = 3 is on the line.

the value of y for the equation of y < -x/3 would have to be less than -1 which would place it in the area below the line.

the graph you create will look like the graph i showed you except you would have shaded the area below the line to indicate that is where the solution to the inequality lies.

unlike an equality solution, the inequality solution will contain many values of y that are less than the value of -x/3.

all those possible solutions will be in the shaded area.

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