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Video: Graphs of Linear Inequalities

Kathryn Kingham

What inequality has been graphed in the given figure?

02:21

Video Transcript

What inequality has been graphed in the given figure?

To solve this problem, thereโ€™s a few things that we need to notice. One of the first things that I noticed is that the line of this function is dotted; it is not a solid line. This tells me that Iโ€™m dealing with the function thatโ€™s greater than or less than. It also tells us thereโ€™s no possibility for greater than or equal to, less than or equal to.

We also notice that our shading is underneath or below our line. Where this function is shaded tells us that ๐‘ฆ has to be less than whatever our function is; the bottom is shaded, so ๐‘ฆ is less than. The only thing left to do is figure out the line thatโ€™s graphed here. What is the function for our line?

In the formula ๐‘ฆ equals ๐‘š๐‘ฅ plus ๐‘, the ๐‘ is the ๐‘ฆ-intercept. Can we use this graph to determine what the ๐‘ฆ-intercept is? The answer is yes. This line crosses the ๐‘ฆ-intercept at point four. The ๐‘ and the ๐‘ฆ-intercept is then four.

Our ๐‘š-value is our slope. Our slope equals the rise over the run, the changes in ๐‘ฆ over the changes in ๐‘ฅ. We can cha- check the rise over run with these two points weโ€™ve been given. The line here is going down four, rise of negative four, and to the right two, for our run of positive two. Our slope is negative four over two. And we can simplify that value to simply negative two.

Once we find the slope, we plug that back into our formula. And weโ€™re left with ๐‘ฆ is less than negative two ๐‘ฅ plus four. This graph gave us all the information we needed to find the formula, ๐‘ฆ is less than negative two ๐‘ฅ plus four.