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Find a linear inequality with the following solution set. Each grid line represents one unit.


http://latex.artofproblemsolving.com/6/4/d/64d8e4d2124c96770af292773d0a587a247b8718.png

(Give your answer in "standard form"  or  where   and  are integers with no common factor greater than 1.)

 Jun 1, 2019
 #1
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Equation of the red line is     y = -x +1

the shaded area PLUS the included red line :    y <= -x+1

 

 

Formatted:    y+x -1 <= 0      or   -y-x+1>=0

 Jun 1, 2019
edited by Guest  Jun 1, 2019
edited by Guest  Jun 1, 2019
 #2
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Noticing that the slope of the line is -1 and the y intercept is 1, the equation of the line in slope intercept form is y=-x+1.

The point (0,0) should work in this inequality, so to make this an inequality this point should be plugged in and then the equals sign adjusted so it is true.

0=-0+1

0=1

This is not true so it should be \(0 \leq 1\), the less than or equil part because the points on the line should work in the inequality.

\(y \leq -x+1\)

To change this into standard form, the -x needs to be moved to the other side.

\(y+x \leq 1\)

This cannot be simplified further so \(\boxed{y+x \leq 1}\) is the answer.

 

It looks like there is another AoPSer on this site smiley

 Jun 1, 2019
 #3
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Give your answer in "standard form"  ax+by+c>0  or   ax+by+c>=0 and a b c are integers with no common factor other than 1. I’m sorry I forgot about the format. Help! How do I convert it?

 Jun 1, 2019
edited by Guest  Jun 1, 2019

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