How do you graph the inequality #2x <3y +6#?

1 Answer
Jun 20, 2018

Answer:

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: #y = 0#

#2x = (3 * 0) + 6#

#2x = 0 + 6#

#2x = 6#

#(2x)/color(red)(2) = 6/color(red)(2)#

#x = 3# or #(3, 0)#

For: #y = -2#

#2x = (3 * -2) + 6#

#2x = -6 + 6#

#2x = 0#

#(2x)/color(red)(2) = 0/color(red)(2)#

#x = 0# or #(0, -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+2)^2-0.035)((x-3)^2+y^2-0.035)(2x-3y-6)=0 [-10, 10, -5, 5]}

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

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

graph{(2x-3y-6) < 0 [-10, 10, -5, 5]}