Video: Graphs of Linear Inequalities

Video Transcript

Write the inequality that has been graphed in the given figure.

Here we can see that we have a linear inequality. It’s a line. Now I also notice that this is a dash line. Since it’s a dash line, that means this inequality will be a less than or greater than. If it were a solid line, it would have been a less than or equal to, or a greater than or equal to sign can be used. So that means we now we’re gonna be using a less than or a greater than sign.

Now notice looking at our line left to right it’s increasing, and all of the shaded region is underneath that line. So if it were underneath the line, that means it would be everything less than that line, so we know that our inequality will be 𝑦 is less than. And we have to figure out the rest, so we have to figure out what is this line.

So we need to find the slope and we need to find 𝑏, the 𝑦 intercept. So our slope can be found by looking at two points on our line and using it to see the rise over the run. So we went up four spaces and then we had to run one space to the right, so our slope is four over one.

Now our 𝑦 intercept, 𝑏, is where we cross the 𝑦-axis, and we cross that at negative three. Therefore, 𝑏 is negative three. Therefore, the inequality that has been graphed in this given figure is 𝑦 is less than four 𝑥 minus three.