### Video Transcript

What inequality has been graphed in the given figure?

To solve this problem, thereโs 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 Iโm dealing with the function thatโs greater than or less than. It also tells us thereโs 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 ๐ฆ has to be less than whatever our function is; the bottom is shaded, so ๐ฆ is less than. The only thing left to do is figure out the line thatโs graphed here. What is the function for our line?

In the formula ๐ฆ equals ๐๐ฅ plus ๐, the ๐ is the ๐ฆ-intercept. Can we use this graph to determine what the ๐ฆ-intercept is? The answer is yes. This line crosses the ๐ฆ-intercept at point four. The ๐ and the ๐ฆ-intercept is then four.

Our ๐-value is our slope. Our slope equals the rise over the run, the changes in ๐ฆ over the changes in ๐ฅ. We can cha- check the rise over run with these two points weโve 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 weโre left with ๐ฆ is less than negative two ๐ฅ plus four. This graph gave us all the information we needed to find the formula, ๐ฆ is less than negative two ๐ฅ plus four.