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Interpreting linear models | Worked example

Sal Khan works through a question on interpreting linear models from the Praxis Core Math test.

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Video transcript

- [Presentor] We're told the graph above, and I put the graph here to the left so that we can see it on the screen. The graph above shows the average annual cost tuition, fees, room and board of a US 4-year public college from 2000 to 2010. A line of best fit is also shown. Based on this trend, which of the following is the best prediction of when the average annual cost will reach $20,000? So pause this video and see if you can answer it. All right. Now, let's do this together. So what they did is these dots here, each of these data points show that, "Okay, in 2000, the year 2000, "it looks like the tuition was close to $12,000 "but not quite 12,000." Then in 2001, it looks like it crossed the $12,000. It's a little more than that but less than 13,000. And it's almost 13,000 in 2002. And they did these data points all the way from 2000 to 2010, and then they tried to fit a line to the data points. And then that's what this line of best fit actually is doing. And then they're essentially asking us to use this line of best fit to extrapolate, to figure out when to predict when the average annual tuition cost will reach $20,000. Now, there's two ways you could do this. You could try to continue this graph and do it visually and then continue it up here and have a marker here for $20,000 and then see when it intersects. It would be some place out here, and try to estimate that. Or what you could do is look at the slope of the line and say, "Okay. Every year, "how much does this tuition go up "every year that goes by?" Or for this one, it looks like if I were to start, let me do this in a color you can see. If I were to start here, it looks like for every two years that go by, at least the line would predict a $1,000 increase in tuition. Every two years that go by, roughly a $1,000 increase in tuition. Two years go by, a $1,000 increase in tuition. Two years go by, a $1,000 increase in tuition. I'm getting very repetitive. So one way to think about it is you could even try to do a bit of a table here to continue that extrapolation where you could say, "All right. So this is year, "and then you have tuition." So we know that in 2010, the tuition is let's just call it $17,000. So the year 2010, the tuition is $17,000. And so we know every time, at least this line of best fit predicts that every time two years passes, the tuition will go up by $1,000. Let's add two years to this, so 2012. So I'm adding two to that. I'm going to add two to that. And then we would expect that a tuition goes up by $1,000. So we would get to $18,000. Then we can do that again. We can go to 2014. We would expect this to go up by another $1,000. So $19,000. And then we add another two years, 2016. And then we'd expect our tuition to go up by $1,000 again. And then we got to the magic number. We want to see when will the average annual cost be $20,000? Based on the line of best fit, it looks like that will happen in 2016.