Before we graph the points on a coordinate plane we will name them:
Solutions:& A: (- 1,3), B: (0,- 1), C: (0,1)
Not solutions:& D: (1,1), E: (0,0), F: (0,- 1)
The points that are solutions we color red and the points that are not we color blue.
For the red points to be included in the solution set, they have to be a part of the shaded area of our inequality. Let's draw a line through D with a negative slope that includes A, B and C when we shade the region above the line.
The three points A, B and C are definitely part of the solution set to this inequality. But so is D as it sits on the boundary line which is solid. To exclude D we can simply dash the boundary line.
This inequality satisfies the two properties. To write it algebraically we need the equation of the boundary line in slope-intercept form:
y=mx+c
We see that it intercepts the y-axis at (0, 1) so c= 1. To find the slope, we count the number of steps the line decreases as we move on step to the right on the x-axis.
As we move one step to the right, the graph falls by 1 which means the slope is - 1. Since the shading is above the boundary line, we are going to use the symbol >. Pulling it all together, we get the inequality:
y> - x+1.
