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## 8th grade (Illustrative Mathematics)

### Course: 8th grade (Illustrative Mathematics) > Unit 6

Lesson 5: Lesson 6: The slope of a fitted line# Scatter plot: smokers

In a negative linear association, as one variable goes up, the other variable goes down at a constant rate. In this case, the percent of adults who smoke drops 0.5% each time the year goes up. In the right graph, the points go down by about 0.5% each year. There should be no points far away from the main trend. Created by Sal Khan.

## Want to join the conversation?

- At 00:9, sal says linear association what does that mean?(7 votes)
- The scatter plot looks like a linear function. It is almost a straight line.(17 votes)

- This is hard is there an easier way to do this.??(6 votes)
- Stick with it! You'll get it. What may help is to brush up on basic shapes of functions (ie: linear= straight line, logarithmic, exponential, polynomial, etc). These are taught in Pre-Calc and Calc classes already. A suggestion to Khan Academy might be to do a quick video and practice review section at the beginning of this section to review what linear/ non-linear functions look like in graph (non-scatter) form...and since I suggested it, I'll even do the video if you want me to, just show me the tools and code to upload the wmv. :-)(18 votes)

- anyone from 2022 i understand perfectly(11 votes)
- At1:02, what does Sal mean by an outlier in the graph?(3 votes)
- Something that doesn't fit in with the rest of the points(10 votes)

- Who here is from the year 10239786413?(7 votes)
- I'm from India.

I also see some people smoking for a living. Really they should stop.

anyways, nice video! :)(8 votes) - Me and my monkey(5 votes)
- Wait so how would you just identify a linear or not linear if 2 look the same like graph 1 and graph 2.(3 votes)
- Graph 1 and graph 2 are both linear. You cannot identify them with linear association.

Instead, in the question, it said that percent drops by 0.5 point each year.

You have to compare two different points and figure it out.(5 votes)

- what is a linear line(2 votes)
- That sounds redundant, a linear function creates a line. The exception to the function is an x=# which is also a line, but not a function.(2 votes)

## Video transcript

The percent of adults
who smoke recorded every few years
since 1967 suggests a negative linear
association with no outliers. On average, the percent drops
by 0.5 points each year. Which of the following plots
suits the above description? So let's see, this looks like
a negative linear association. As the years go by, you have a
smaller percentage of smokers. This one does too. As years go by, you have
the number of smokers go down and down. This one down here
also looks like that, although it's not as smooth. If you were to fit
a line here, it looks like you have
a few outliers. Well, this is a
positive correlation. So we can definitely
rule out Graph 4. Now, the other
thing that they told us is that there
are no outliers, suggests a negative linear
association with no outliers. If you were to try to
fit a line to Graph 3, you could fit a line
pretty reasonably. That would go
someplace like that. But it would have this
outlier right over here. It looks like it's 12
or 13 years after 1967. So that would be 1980. It looks like an outlier there. But they said it didn't
have any outliers. So we would rule out Graph 3. And so we have to pick
between Graph 1 and Graph 2. So the other hint they give
us or piece of data they give us is that the percent
drops by 0.5% each year. So here's what's happening. In 1967, it looks like
we're at about 55%. And then 10 years go by. We are roughly at around
45, a little under 45%. So we dropped 10% in 10 years. That seems to be how much
this is dropping, roughly 10% in 10 years. Another 10 years go by. We go from 45, a little
more than 10% in 10 years. And so that would mean that
we're dropping, on average, more than one percentage
point per year. That seems more than
what's going on here. Now, let's look over here. Over here, we're starting,
it looks like, at around 42%. And then after 10 years,
it looks like we're at 37%. So it looks like
we've dropped about 5% in 10 years, which is
consistent with this. If you drop 5% in
10 years, that means you drop half a
percent per year. So we'll go with Graph 2.