The Slope of a Fitted Line

The Slope of a
Fitted Line

Lesson 6

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2019 Open Up Resources |

Today’s
Goal

❏ I can use the slope of

a line fit to data in a
scatter plot to say
how the variables are
connected in
real-world situations.

Estimating Slope

Activate: Warm Up
Activity 6.1
● Think Pair Share

Estimate the
slope of the line.

Begin working on
your own. (1 min)

It’s better to use
points that are far
apart rather than
close together when
estimating slope!

Interpreting Slopes

Comprehend/Apply: Activity 6.3
● MLR8: Discussion Supports

An equation for the line is y = -0.073x + 17,404.485.
What is the slope? What does that slope tell us?

​m = -0.073

For every increase of 1 mile, the price of the car decreases by $0.073.

y = 5,520.619x – 1,091.393

● What is the meaning of the slope?

​If the weight of the diamond increases by one carat, the price increases by $5, 521.

Multiple Choice

The equation y = 0.85x + 0.09 is an approximation of the line of best fine for the data on the scatterplot. Which statement correctly describes the meaning of the slope of this line?

• Each player made about 85% of the free throws that were attempted.

• In each game, players attempted free throws during 85% of the playing time.

• Each player attempted free throws in 85% of the games that were played.

• In each game, about 85% of the players who attempted free throws made them.

y = -0.011x + 40.604

● What is the meaning of the slope?

​If the car increases by 1 kg, the fuel efficiency decreases by 0.011 mpg.

Multiple Choice

Jamin measured the depth of the snow in his front yard for 7 days. An equation for the line of best fit for Jamin's data is y = -0.5x + 8. Let x represent the number of days. Let y represent the depth of the snow in inches.

Which statement best describes the meaning of the slope in this equation?

• The depth of the snow decreased by 0.5 inch per day.

• The depth of the snow increased by 0.5 inch per day.

• The depth of the snow decreased by 8 inches per day.

• The depth of the snow increased by 8 inches per day.

The model for energy
consumption and
temperature predicted a
0.59 kilowatt hour increase
in energy consumption
every 1 degree increase in
temperature.

y = 0.59x – 21.912

​Estimate how much the temperature would need to increase to raise energy consumption by 6 kilowatt hours. Substitute x = 6.

Multiple Choice

An equation for a line of best for these is y = -0.13x + 24.04, where y represents the height of the water in the lake, and x represents the day. Using the line of best fit, which of the following is the best estimate of the height of the water in the lake on Day 14?

• 22.2

• 22.4

• 24.1

• 25.9

What was the easiest way
to find the slope for each
situation?

What is the difference between a
positive and negative slope in
your interpretations?

Positive or Negative

Comprehend/Apply: Activity 6.4
● MLR1: Stronger and Clearer Each Time

linear
associations

A linear association is present
when the points in a scatter
plot suggest that a linear
model would fit the data well.

Still other data sets have
no association when the data
appears random and no curve
would represent the data well.

In this activity…

identify if the data has a
linear association or not.

If it does, what type of
slope would it have?

Which of these
scatter plots show
evidence of…

● a positive

association?

● a negative

association?

● no association?

Dropdown

A linear model would fit and have a ​

Select answer

slope.

Drag and Drop

A linear model would fit and have a ​

Placeholder

slope.

Drag these tiles and drop them in the correct blank above

positive

negative

no

Dropdown

A linear model would fit and have a ​

Select answer

slope.

Multiple Choice

A linear model would not fit very well.

• TRUE

• FALSE

Multiple Choice

A linear model would fit and have a positive slope, even though it has an outlier.

• TRUE

• FALSE

What strategy did you
use to determine if
the data had a linear
association?

Would you be able to
notice a linear
association from the
data in a table?

Organize: Activity Synthesis

What does it mean to
have a positive
association?

How did you
determine if the data
had a positive
assoication?

What are other pairs
of things that you
conjecture would
have a negative,
linear association?

Let’s
synthesize
our learning!

How would you describe the trend in the
scatter plot?

As the height
of a dog
increases, its
weight tends
to increase!

Organize: Lesson Synthesis

The slope of a fitted line is 4.25. What
does that tell us about the dogs?

For every 1
inch increase
in dog height,
the predicted
weight is 4.25
pounds.

Today’s
Goals

❏ I can use the slope of a

line fit to data in a
scatter plot to say how
the variables are
connected in real-world
situations.

Trends in the Price
of Used Cars

Apply/Summarize
Cool Down Activity 6.5

6-6-5: Trends in the Price of Used Cars

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