How do you graph the inequality #6x + 4y ≤ 24#?

Question

3967 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-15T15:18:13

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#

#(6 * 0) + 4y = 24#

#0 + 4y = 24#

#4y = 24#

#(4y)/color(red)(4) = 24/color(red)(4)#

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

For: #y = 0#

#6x + (4 * 0) = 24#

#6x + 0 = 24#

#6x = 24#

#(6x)/color(red)(6) = 24/color(red)(6)#

#x = 4# or #(4, 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.

The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y-6)^2-0.125)((x-4)^2+y^2-0.125)(6x+4y-24)=0 [-20, 20, -10, 10]}

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

graph{(6x+4y-24) <= 0 [-20, 20, -10, 10]}