Video Transcript
What is the inequality graphed in the given figure?
Well, what our inequality is showing us is that we’re interested in everything above. Then, we’ve got the dotted line. So, what does this actually mean? Well, the first thing we want to do is we want to find the equation of the line that goes through two. Well, as the line is a horizontal line, we can see that one of the coordinates remains the same throughout if we picked any point along that line, and that would be the 𝑦-coordinate, because we can see that along the line, any point we pick will give us a 𝑦-coordinate of two.
Say, for instance, I’ve shown here a couple of points. We’ve got negative three, two and two, two. And what this means is that the equation of this line is gonna be 𝑦 equals two. Now, what we’re looking for is the inequality. So, we want to find the region that’s above the line 𝑦 equals two. Well, before we can actually write down our inequality, first of all, we need to see what is the significance of the dotted or dashed line.
Well, if we remind ourselves, the dotted or dashed line means that it’s gonna be greater than or less than, whereas a solid line would be greater than or equal to or less than or equal to, remembering though on an inequality sign, it’s the line underneath that tells us it can be or equal to. Now just to remind us how to use our inequality signs, we remember that the large open end is always pointing towards the bigger number and the end that’s closed or pointed, points toward the smallest number.
So, therefore, because we have a dashed line and because we want everything above that dashed line, we can say that the inequality graphed is 𝑦 is greater than two.
