Question 127093This question is from textbook Beginning Algebra
: Graph the inequality
y>=1
I do not understand how to begin this problem
This question is from textbook Beginning Algebra
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Step 1, create a graph of the line y = 1. Since there is no x component to the equation, this describes the set of all possible points where y = 1 and x can be anything you want -- in other words, a horizontal line one unit above the x-axis.
Now that you have created your line, you need to decide whether it should be a dashed line or a solid line. A dashed line means that the points actually on the line are NOT included in the solution set to the equation, a solid line means that the points actually on the line ARE included. Since your inequality has an 'or equal' component, the points of the line ARE included and you should be making a solid line.
The only thing left is to determine which side of the line to shade, indicating the half-plane of points that make the relation true. The process is to pick a point NOT on the line. It doesn't matter which side of the line the chosen point lies, just as long as it isn't a point actually on the line. Next you substitute the coordinates of the chosen point into your inequality. If the result is a true statement, then you have chosen a point on the 'correct' side of the line and that is the side that should get shaded. On the other hand, if your selected point results in a false statement, your selected point is on the 'wrong' side of the line, so you shade in the other side.
For your example, let's just choose something easy, like the origin, (0,0). This point is below the line. Substitute the y-coordinate of the chosen point into the inequality -- that's all you can do here because there is no x component -- and you get  . Now this statement is clearly false, so the point (0,0) is on the wrong side and you should shade in the half plane above the line.
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