How do you graph #6x+3y<=18#?

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Answer 1 · 2018-01-26T22:43:29

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#

#(6 * 0) + 3y = 18#

#0 + 3y = 18#

#3y = 18#

#(3y)/color(red)(3) = 18/color(red)(3)#

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

For: #y = 0#

#6x + (3 * 0) = 18#

#6x + 0 = 18#

#6x = 18#

#(6x)/color(red)(6) = 18/color(red)(6)#

#x = 3# 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 a solid line because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y-6)^2-0.125)((x-3)^2+y^2-0.125)(6x+3y-18)=0 [-20, 20, -10, 10]}

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

graph{(6x+3y-18) <= 0 [-20, 20, -10, 10]}