How do you graph the inequality #y<=-4x+12#?

1 Answer
smendyka
Nov 15, 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#

#y = (-4 xx 0) + 12#

#y = 0 + 12#

#y = 12# or #(0, 12)#

For: #x = 3#

#y = (-4 xx 3) + 12#

#y = -12 + 12#

#y = 0# or #(3, 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-12)^2-0.25)((x-3)^2+y^2-0.25)(y+4x-12)=0 [-30, 30, -15, 15]}

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

graph{(y+4x-12) <= 0 [-30, 30, -15, 15]}

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