How do you graph #-4x+y> -6#?

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Answer 1 · 2018-07-28T11:33:25

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#

#(-4 * 0) + y = -6#

#0 + y = -6#

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

For: #x = 2#

#(-4 * 2) + y = -6#

#-8 + y = -6#

#-8 + color(red)(8) + y = -6 + color(red)(8)#

#0 + y = 2#

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

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+6)^2-0.08)((x-2)^2+(y-2)^2-0.08)(-4x+y+6)=0 [-20, 20, -10, 10]}

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

However, we need to change thee boundary line to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(-4x+y+6) > 0 [-20, 20, -10, 10]}