How do you graph the inequality #x+8y>16#?

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Answer 1 · 2018-03-04T14:45:37

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 + 8y = 16#

#8y = 16#

#(8y)/color(red)(8) = 16/color(red)(8)#

#y = 2# or #(0, 2)#

For: #x = 8#

#8 + 8y = 16#

#-color(red)(8) + 8 + 8y = -color(red)(8) + 16#

#0 + 8y = 8#

#8y = 8#

#(8y)/color(red)(8) = 8/color(red)(8)#

#y = 1# or #(8, 1)#

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-2)^2-0.025)((x-8)^2+(y-1)^2-0.025)(x+8y-16)=0 [-10, 10, -5, 5]}

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

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

graph{(x+8y-16) > 0 [-10, 10, -5, 5]}