How do you graph the linear inequality #-2x - 5y<10#?

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Answer 1 · 2018-03-13T16:18:27

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#

#(-2 * 0) - 5y = 10#

#0 - 5y = 10#

#-5y = 10#

#(-5y)/color(red)(-5) = 10/color(red)(-5)#

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

For: #y = 0#

#-2x - (5 * 0) = 10#

#-2x - 0 = 10#

#-2x = 10#

#(-2x)/color(red)(-2) = 10/color(red)(-2)#

#x = -5# or #(-5, 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.

graph{(x^2+(y+2)^2-0.05)((x+5)^2+y^2-0.05)(-2x-5y-10)=0 [-10, 10, -5, 5]}

Now, we can shade the rightside of the line.

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

graph{(-2x-5y-10) < 0 [-10, 10, -5, 5]}