Home > Algebra > Linear Inequalities in Two Variables

How do you graph #2x-y<6#?

Answer 1

Leave #y# alone for better readability.

#2x-6 < y# which is equivalent to:

#y>2x-6#

First, graph #y=2x-6# but since #y!=2x-6# the line should be a dashed line. That dahsed line will divide the coordinate plane into two. Select #2# random points from each part.

Lets say #A(0,0)# and #B(5,0)#

Plug these to the inequality to see which part of the coordinate plane is satisfying this inequality.

#A:0>-6# correct #B:0>4# incorrect

So the part where #A# lies will be shaded.

graph{y>2x-6 [-10, 10, -5, 5]}

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Ethan Adkins

To graph the inequality 2x - y < 6:

Graph the boundary line: 2x - y = 6
Choose a test point not on the boundary line and substitute its coordinates into the original inequality.
If the test point satisfies the inequality, shade the region containing it. If not, shade the opposite region.
The shaded region represents the solution set.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you graph #2x-y&lt;6#?

How do you graph #2x-y<6#?