How do you graph #5x-2y<10#?

1 Answer
smendyka
Oct 4, 2017

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: #x = 0#

#(5 * 0) - 2y = 10#

#0 - 2y = 10#

#-2y = 10#

#(-2y)/color(red)(-2) = 10/color(red)(-2)#

#y = -5# or #(0, -5)#

For: #x = 2#

#(5 * 2) - 2y = 10#

#10 - 2y = 10#

#-color(red)(10) + 10 + 2y = -color(red)(10) + 10#

#0 - 2y = 0#

#-2y = 0#

#(-2y)/color(red)(-2) = 0/color(red)(-2)#

#y = 0# or #(2, 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.

graph{(x^2+(y+5)^2-0.125)((x-2)^2+y^2-0.125)(5x-2y-10)=0 [-20, 20, -10, 10]}

We can now graph the inequality. Because there is no "or equal to" clause in the inequality operator we will make the line a dashes line. And, we can shade the left side of the line for the "less than" inequality operator.

graph{5x-2y-10 < 0 [-20, 20, -10, 10]}

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