How do you graph #4x-5y-10<=0#?

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Answer 1 · 2018-06-03T21:00:04

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#

#(4 * 0) - 5y - 10 = 0#

#0 - 5y - 10 + color(red)(10) = 0 + color(red)(10)#

#-5y - 0 = 10#

#-5y = 10#

#(-5y)/color(red)(-5) = 10/color(red)(-5)#

#y = -2# or #(0, -2)#

For: #x = 5#

#(4 * 5) - 5y - 10 = 0#

#20 - 5y - 10 + color(red)(10) = 0 + color(red)(10)#

#20 - 5y - 0 = 10#

#20 - 5y = 10#

#20 - color(red)(20) - 5y = 10 - color(red)(20)#

#0 - 5y = -10#

#-5y = -10#

#(-5y)/color(red)(-5) = -10/color(red)(-5)#

#y = 2# or #(5, 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.

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

graph{(x^2+(y+2)^2-0.035)((x-5)^2+(y-2)^2-0.035)(4x-5y-10)=0 [-10, 10, -5, 5]}

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

graph{(4x-5y-10) <= 0 [-10, 10, -5, 5]}