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.)

Guest Jun 1, 2019

#1**0 **

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

Guest Jun 1, 2019

edited by
Guest
Jun 1, 2019

edited by Guest Jun 1, 2019

edited by Guest Jun 1, 2019

#2**0 **

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

power27 Jun 1, 2019