How do you graph the inequality #y+4x>=3#?

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Answer 1 · 2017-09-04T15:13:16

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#

#y + (4 * 0) = 3#

#y + 0 = 3#

#y = 3#

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

For: #x = 2#

#y + (4 * 2) = 3#

#y + 8 = 3#

#y + 8 - color(red)(8) = 3 - color(red)(8)#

#y + 0 = -5#

#y = -5# or #(2, -5)#

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 a "or equal to" clause.

graph{(x^2+(y-3)^2-0.05)((x-2)^2+(y+5)^2-0.05)(4x+y-3)=0 [-15, 15, -7.5, 7.5]}

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

graph{(4x+y-3)>=0 [-15, 15, -7.5, 7.510]}