How do you graph the inequality #2x + y ≤ 4#?

1 Answer
smendyka
Oct 26, 2017

See a solution process below:

Explanation:

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

For: #x = 0#

#(2 * 0) + y = 4#

#0 + y = 4#

#y = 4#

#y = 4# or #(0, )#

For: #x = 2#

#(2 * 2) + y = 4#

#4 + y = 4#

#-color(red)(4) + 4 + y = -color(red)(4) + 4#

#0 + y = 0#

#y = 0# or #(2, 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.
The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y-4)^2-0.125)((x-2)^2+y^2-0.125)(2x+y-4)=0 [-20, 20, -10, 10]}

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

graph{(2x+y-4)<=0 [-20, 20, -10, 10]}

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