Find a linear inequality with the following solution set. Each grid line represents one unit.
(Give your answer in the form \(ax+by+c>0 \) or \(ax+by+c\geq0 \) where \(a, b \) and \(c\) are integers with no common factor greater than 1.)
First, find the equation of the red line.
The slope is 1, the y-intercept is 1, so the equation of the line is y = 1x + 1, or just y = x + 1.
Since the line is dashed, it will either be y > x + 1 or y < x + 1.
To find out which one, let's test a point from the shaded area. I'm going to pick the point (1, 3).
Substituting 1 for x, and 3 for y, we see that 3 > 1 + 1 is true; so we should pick y > x + 1.
Had we tested y < x + 1, we would have gotton 3 < 1 + 1, which is false; this would tell us not to
choose this possible answer.
We have chosen y > x + 1; now, we need to put it into correct form.
Starting with: y > x + 1, we can get: -x + y - 1 > 0.