Find a linear inequality with the following solution set. Each grid line represents one unit.
https://latex.artofproblemsolving.com/b/d/c/bdc17544a660a2ede75d5c2642f86c2311ec1028.png
The dotted line passes through (4, -3) and (3, -4) ,
so its slope = \(\frac{-4--3}{3-4}\) = \(\frac{-1}{-1}\) = 1
Using the point (4, -3) and the slope 1 , the equation of the dotted line is
y - -3 = 1(x - 4)
y = x - 4 - 3
y = x - 7
We want our inequality's solution set to be all points on one side of this line. It will be either
y > x - 7 or y < x - 7
Since we want (0, 0) to be a solution, let's test that point to find the right one.
0 > 0 - 7 or 0 < 0 - 7
0 > -7 this is true. 0 < -7 this is false.
The inequality that has (0, 0) as a solution is the one we want....that is
y > x - 7
The dotted line passes through (4, -3) and (3, -4) ,
so its slope = \(\frac{-4--3}{3-4}\) = \(\frac{-1}{-1}\) = 1
Using the point (4, -3) and the slope 1 , the equation of the dotted line is
y - -3 = 1(x - 4)
y = x - 4 - 3
y = x - 7
We want our inequality's solution set to be all points on one side of this line. It will be either
y > x - 7 or y < x - 7
Since we want (0, 0) to be a solution, let's test that point to find the right one.
0 > 0 - 7 or 0 < 0 - 7
0 > -7 this is true. 0 < -7 this is false.
The inequality that has (0, 0) as a solution is the one we want....that is
y > x - 7