How do you graph #y < x/3#?

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Answer 1 · 2018-05-17T01:43:50

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 = 3#

#y = 3/3#

#y = 1# or #(3, 1)#

For: #x = 6#

#y = 6/3#

#y = 2# or #(6, 2)#

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-3)^2+(y-1)^2-0.05)((x-6)^2+(y-2)^2-0.05)(y-(x/3))=0 [-10, 10, -5, 5]}

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

We also need to change the boundary line to be a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(y-(x/3)) < 0 [-10, 10, -5, 5]}