How do you graph the inequality #-2 x + y> -5#?

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Answer 1 · 2018-05-29T12:16:48

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) + y = -5#

#0 + y = -5#

#y = -5# or #(0, -5)#

For: #x = 2#

#(-2 * 2) + y = -5#

#-4 + y = -5#

#color(red)(4) - 4 + y = color(red)(4) - 5#

#0 + y = -1#

#y = -1# or #(2, -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+5)^2-0.125)((x-2)^2+(y+1)^2-0.125)(-2x+y+5)=0 [-20, 20, -10, 10]}

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

We also need to change the boundary line to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(-2x+y+5) > 0 [-20, 20, -10, 10]}