How do you graph the inequality #x + y <6#?

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Answer 1 · 2018-03-28T11:45:12

See a solution process below:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For: #x = 0#

#0 + y = 6#

#y = 6# or #(0, 6)#

For: #y = 0#

#x + 0 = 6#

#x = 6# or #(6, 0)#

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{(x^2+(y-6)^2-0.125)((x-6)^2+y^2-0.125)(x+y-6)=0 [-20, 20, -10, 10]}

Now, we can shade the left side of the line.

The boundary line will be changed to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(x+y-6) < 0 [-20, 20, -10, 10]}