How do you graph the inequality #8x+y<=6#?

1 Answer
Oct 8, 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#

#(8 * 0) + y = 6#

#0 + y = 6#

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

For: #x = 2#

#(8 * 2) + y = 6#

#16 + y = 6#

#-color(red)(16) + 16 + y = -color(red)(16) + 6#

#0 + y = -10#

#y = -10# #(2, -10)#

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-6)^2-0.25)((x-2)^2+(y+10)^2-0.25)(8x+y-6)=0 [-30, 30, -15, 15]}

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

graph{(8x+y-6) <= 0 [-30, 30, -15, 15]}