How do you graph the inequality #10x+2y<=14#?

1 Answer
smendyka
Aug 23, 2017

See a solution process below:

Explanation:

First, solve for two points as an equation instead of a inequality to find the boundary line for the inequality.

For #x = 0#

#(10 * 0) + 2y = 14#

#0 + 2y = 14#

#2y = 14#

#(2y)/color(red)(2) = 14/color(red)(2)#

#y = 7# or #(0, 7)#

For #x = 2#

#(10 * 2) + 2y = 14#

#20 + 2y = 14#

#-color(red)(20) + 20 + 2y = -color(red)(20) + 14#

#0 + 2y = -6#

#2y = -6#

#(2y)/color(red)(2) = -6/color(red)(2)#

#y = -3# or #(2, -3)#

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-7)^2-0.125)((x-2)^2+(y+3)^2-0.125)(10x+2y-14)=0 [-20, 20, -10, 10]}

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

graph{(10x+2y-14)<=0 [-20, 20, -10, 10]}

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