8th Grade Winter Break Tutorials Trend Lines, Slope and Graphing

Scatter Plots and Trend Lines

Moody

Three Types of Scatter Plots

• Positive Correlation

• Negative Correlation

• No Correlation

Positive Correlation

• The higher the drop height the higher the bounce height

No Correlation

• There is no relationship between hair color and shoe size

Negative Correlation

• The longer a car is driven and the lower the gasoline level

Multiple Choice

What is the type of correlation for this scatter plot?

• positive

• negative

• none

Multiple Choice

What is the type of correlation for this scatter plot?

• positive

• negative

• none

If a carpenter earned $1000, what is the estimate for how many days he worked?

Multiple Choice

Which sentence describes the relationship shown on this scatter plot?

• As the temperature decreases, the visitors increase.

• As the temperature decreases, the visitors increase.

• As the temerature increases, the vistiotrs increase.

• no correlation

Multiple Choice

The number of siblings you have and your weight would have which type of correlation?

• none

• positive

• negative

Multiple Choice

A teacher made the following graph showing the number of hours that a student studied for an exam versus their exam grade. Predict the grade of a student if they studied for 3.5 hours.

• 60

• 70

• 75

• 90

Scatter Plots with Trend Lines

also called line of best fit or regession line

Multiple Choice

Which trend line matched the scatter plot best?

• A

• B

• C

Multiple Choice

Which trend line matched the scatter plot best?

• A

• B

• C

• D

Multiple Choice

Which trend line matched the scatter plot best?

• A

• B

• C

• D

The red line represents the line of best fit for the scatter plot. How many ice cream sales are expected if the temperature is 90°?

​

Multiple Choice

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books. Use the trend line to predict how many chapters would be in a book with 140 pages.

• 12 chapters

• 14 chapters

• 19 chapters

• 21 chapters

Multiple Choice

The graph shows a line of best fit for data collected on the amount of income earned by lawn companies in relation to the number of yards mowed. What is the equation of the trend line?

Look at the scale on each axis.

• $$y=\frac{3}{2}x$$

• $$y=30x$$

• $$y=300x$$

Multiple Choice

As x increases, y decreases.

• no correlation
• negative correlation
• correlation coefficient
• positive correlation

Multiple Choice

As x increases, y increases

• correlation coefficient
• causation
• positive correlation
• negative correlation

Multiple Choice

What type of association does this graph have?

• positive
• negative
• none
• all of the above

Multiple Choice

What is the type of association?

• Negative 
• no association
• positive 

Multiple Choice

What type of correlation?
The temperature outside and the amount of ice cream sales. 

• Positive correlation
• Negative correlation
• No correlation

Multiple Choice

Which scatter plot shows a linear relationship between x and y?

• Graph A

• Graph B

• Graph C

• Graph D

Multiple Choice

The scatter plot below shows the number of books read by students in Mrs. Hall’s English class and their final grades. Which statement represents the best description about the line of best fit?

• The more books students read, the lower their English grade.
• The more books students read, the higher their English grade.
• The fewer books students read, the higher their English grade. 
• No relationship exists between the number of books students read and their English grades. 

Multiple Choice

Which best describes the form of this scatterplot?

• linear
• nonlinear
• scattered

Multiple Choice

What is a line of best fit used for?

• To make predictions
• To make the graph look pretty
• To connect the points
• To make it look like you know what you are doing

Multiple Choice

What type of association does this scatter plot show?

• positive linear association

• negative linear association

• no association

• nonlinear association

Multiple Choice

Which sentence describes the relationship shown on this scatter plot?

• As the temperature decreases, the visitors increase. 
• As the temperature increases, the number of visitors increases. 
• As the visitors increase, the temperature decreases. 
• No correlation

Scatterplots and Trend Lines

8th Grade

What is a Trend Line?

When data is collected, points do not form a straight line, but they may approximate to a linear relationship

A trend line is a line that is

VERY CLOSE to most of the data points.

It is used to make conjectures (predictions)

Multiple Choice

What is a trend line used for?

• To make predictions

• To make the graph look pretty

• To connect the points

First, Lets make a trend line!

- Count the number of points, make a line that best fits the data points.

TIP: Count the number of total points. Try to have the same number of points on both sides of the trend line

Make a Prediction!

How many visitors would the beach have at 90 degrees?

Make a prediction!

What will the weight of the shipment be for 7 books?

Multiple Choice

Which graph shows a line of best fit (trend line) for the scatter plot?

• Graph A

• Graph B

• Graph C

• Graph D

Multiple Choice

Which of the following lines represents the line of best fit for the scatter plot?

• A
• B
• C
• D

Multiple Choice

Based on the scatterplot, what is the best prediction of the average number of hours a person spends at work every week, if that person spends an average of 10 hours on recreational activities every week?

• 33 hours
• 85 hours
• 50 hours
• 65 hours

Multiple Choice

Based on the scatterplot, what is the best prediction of the average amount of money spent on groceries for a household of 7 people?

• $240
• $190
• $210
• $300

The following questions are for you to do independently...

Multiple Choice

Based on the trend in the data, approximately how many free throws would a player be expected to make if he attempted 60 free throws?

• 50
• 35
• 25
• 60

Multiple Choice

Based on this scatterplot, approximately what score would a student with 6 absences expect to receive on the final exam?

• 65

• 92

• 67

• 76

Multiple Choice

Based on the scatterplot, about how much money would a group of 10 people be expected to spend on food and beverages at this restaurant?

• $135
• $115
• $105
• $150

Multiple Choice

What is the type of association?

• Negative 
• no association
• positive 

Multiple Choice

What is the correlation between length of running start and distance of jump?

• positive:  the further you run the further you jump
• negative: the less you run the less distance of your jump
• positive: the further your running start the less your distance

Multiple Choice

Which of the following lines represents the line of best fit for the scatter plot?

• A
• B
• C
• D

Multiple Choice

Select the statement that best describes the line.

• The line is the line of best fit.
• The line is NOT a line of best fit because it does not pass through two points.
• The line is NOT a line of best fit because it does not go through the middle of the data set.
• The line is NOT a line of best fit because it does not go through the origin.

Multiple Choice

What type of correlation would you likely see with:

The amount of time spent working compared to the amount of money earned

• positive correlation

• negative correlation

• no correlation

Multiple Choice

Which line appears to fit the data better?

• line A

• line B

Multiple Choice

Which scatterplot shows a negative relationship?

Multiple Choice

Which shows a line of best fit?

Multiple Choice

If m = 8/5 and b = -8/5, what is the equation of the trend line in y= mx + b?

• 0 = 8/5 (1) - 8/5

• y = -8/5 x + 8/5

• y = 8/5 x - 8/5

• y = mx + b

Multiple Choice

If m = -3/4 and b = 9, what is the equation of the trend line in y= mx + b?

• 0 = -3/4 (9) +9

• y = -3/4 x + 9

• y = -3/4 x - 9

• y = 3/4 + 9

Multiple Choice

According to the graph, how many students are in the class?

• 26
• 25
• 15
• 30

Multiple Choice

What type of correlation?
The temperature outside and the amount of ice cream sales. 

• Positive correlation
• Negative correlation
• No correlation

Multiple Choice

The scatter plot below shows the number of books read by students in Mrs. Hall’s English class and their final grades. Which statement represents the best description about the line of best fit?

• The more books students read, the lower their English grade.
• The more books students read, the higher their English grade.
• The fewer books students read, the higher their English grade. 
• No relationship exists between the number of books students read and their English grades. 

Multiple Choice

Choose the scatter plot that best represents this relationship: The number of pets someone owns and the size of their shoes

Multiple Choice

The scatterplot shows the temp, in degrees, outside a house every hour for 10 hours.

Estimate the temp after 13 hours based off the trendline.

• 57.5

• 50

• 10

• 13

• 61.5

Multiple Choice

The slope of the trend line is $\frac{-5}{7}$ 

What does that mean?

• gain 5 hour of sleep for 7 cups of coffee

• lose 5 hours of sleep for 7 cups of coffee

• lose 7 cups of coffee for 5 hours of sleep

• lose 5 cups of coffee for 7 hours of sleep

• gain 7 cups of coffee for every 5 hours of sleep

Multiple Choice

Which of the following could be the equation of the trend line for this graph?

• $y=10x\ -\ 15$

• $y=-3x+12$

• $y=\frac{1}{2}x+11$

• $y=-\frac{4}{3}x$

• There is no trend line because there is no association

Multiple Choice

Which equation could be a trend line for this graph?

• $y=2x$

• $y=2x+5$

• $y=-2x+5$

• $y=-2x$

• There is no trend line because there is no association

Multiple Choice

Which of the following would be the most accurate equation for the scatter plot?

• y = -2x - 7

• y = -x + 7

• y = 3x + 7

• y = 25x + 7

Multiple Choice

What is the slope of this trend line?

• $-\frac{10}{3}$

• $\frac{-70}{3}$

• $\frac{-1}{3}$

• 70

• -3

Multiple Choice

The graph above shows a line of best fit for data collected on the distance bicyclists have remaining in relation to the amount of time they have been riding.  What is the equation of the line of best fit?

• y = -25x + 170
• y = 25x + 170
• y = -(5/8) x + 170
• y = (5/8) x + 170

Multiple Choice

The graph above shows a line of best fit for data collected on the amount earned by waiters and waitresses last week in relation to the number of tables they served.  What is the equation of the line of best fit?

• y = (5/3) x + 375
• y = (1/3) x + 475
• y = (5/3) x + 475
• y = (1/3) x + 375

Multiple Choice

A group of students did an experiment to see how drinking cups of coffee right before bed affected sleep.  The results are shown below in the scatter plot with a line of best fit.  Use the given line of best fit to approximate the rate of change relative to the scatter plot.

• (7/5) hours/cup
• (5/7) hours/cup
• - (7/5) hours/cup
• - (5/7) hours/cup

Multiple Choice

What the y-intercept for the line of best fit for the scatter plot?

• 35

• 50

• 30

• 20

Multiple Choice

The following scatter plot shows Pam's training as she prepares to run a 6 mile race at the end of the month.  Which of the following would be a reasonable approximation for the length of time it would take for her to run 6 miles? 

• A. 50 min
• B. 80 min
• C. 45 min
• D. 60 min

Multiple Choice

What kind of association does the scatter plot show?

• Positive

• Negative

• No association

Multiple Choice

What kind of association does the scatter plot show?

• Positive

• Negative

• No association

Multiple Choice

Mrs. Collins made a scatterplot to show the relationship between the number of absences and a student’s final exam score. Based on this scatterplot, a student with 6 absences should get approximately what score on the final exam?

• 65

• 92

• 70

• 76

Multiple Choice

The graph shows a line of best fit for data collected on the amount of income earned by lawn companies in relation to the number of yards mowed.  What is the equation of the line of best fit?

• y = (3/2) x
• y = 30x
• y = 30x + 300
• y = (3/2)x + 300

Multiple Choice

The graph above shows a line of best fit for data collected on the distance bicyclists have remaining in relation to the amount of time they have been riding.  What is the equation of the line of best fit?

• y = -25x + 170
• y = 25x + 170
• y = -(5/8) x + 170
• y = (5/8) x + 170

Graphing from Standard Form

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Standard Form

Multiple Choice

What is A in this equation?

 $3x\ -\ 4y\ =\ 16$  

• 3

• -4

• 16

• 4

Multiple Choice

What is B in this equation?

 $3x\ -\ 4y\ =\ 16$  

• 3

• -4

• 16

• 4

Multiple Choice

What is C in this equation?

 $3x\ -\ 4y\ =\ 16$  

• 3

• -4

• 16

• 4

Multiple Choice

What is the standard form of a linear equation?

• y = mx + b
• Ax + By = C

Graphing from Standard form

Using Intercepts

Intercepts

The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero. The y-intercept is the point at which the graph crosses the y-axis. At this point, the x-coordinate is zero.

Multiple Choice

What is the x and y intercept for the following equation ?

4x - 10y = 20

• x - int = 4

  y-int = -10

• x-int = 5

  y-int = 2

• x - int = 5

  y int = -2

• x -int = 4

  y -int = -10

Multiple Choice

Find the x and y intercepts
4x - 5y = 40

• x intercept is 10 
  y intercept is 8
• x intercept is 10
  y intercept is 20
• x intercept is 8
  y intercept is 10
• x intercept is 10
  y intercept is -8

Graphing from Standard Form

Using Slope and Intercepts

Multiple Choice

Find the slope and y-intercept of:

2x - 3y = -12

• slope = 2/3, y-intercept = -12

• slope = -2/3, y-intercept = -3

• slope = 2/3, y-intercept = 4

• slope = -12, y-intercept = -3

Multiple Choice

Find the slope and y-intercept of the following:

3x - y = 9

• Slope = 3, y-intercept = -9

• Slope = 9, y-intercept = 3

• Slope = 3, y-intercept = 9

• Slope = -1, y-intercept = 3

Lesson 2: Graphing Slope-Intercept Form

Graphing a linear relationship from slope-intercept form equation

y = mx + b

• What does the equation give us so that we can graph the line?

• 
  

• m = __________

• b =  __________

• Graph the line

y = -x + 2

• m = ___________

• b = ____________

• Graph the line

y = 4

• m = ____________

• b = _____________

• Graph the line

x = 5

• m = ________________

• b = _________________

• Graph the line

Quizizz Practice

Open Graph From Intercept Form in Quizizz

Lesson 2: Graphing Slope-Intercept Form

Graphing a linear relationship from slope-intercept form equation

y = mx + b

• What does the equation give us so that we can graph the line?

• 
  

• m = __________

• b =  __________

• Graph the line

y = -x + 2

• m = ___________

• b = ____________

• Graph the line

y = 4

• m = ____________

• b = _____________

• Graph the line

x = 5

• m = ________________

• b = _________________

• Graph the line

Quizizz Practice

Open Graph From Intercept Form in Quizizz

Graphing Linear Systems

Graph each line.

Use Slope Intercept Form y=mx+b

Multiple Choice

$$y=3/2x-6$$  What do you first on the graph?

• plot a point 6 to the left

• plot a point down 6

• rise 3 run 2

• plot a point up 6

Multiple Choice

Which way do you count the slope 

$$y=-2x+1$$  ?

• down 1 right 2

• down 2 right 1

• down 1 left 2

• down 2 left 1

Multiple Choice

What is the solution?

• (2,-3)

• (-3,-2)

• (3,-2)

• (-3,2)

Write the solution. Look for where the lines intersect. (2,-3)

Multiple Choice

What is the solution?

• No Solution

• Many Solution

• One Solution

Multiple Choice

$$8x+2y=-6$$   $$y=-4x-3$$  

• No Solution

• Many Solution

• One Solution

HOMEWORK

Play the Quizizz games. You can do them multiple times to get higher score.

Graphs of Linear Functions

​

Slope Intercept Form Equation

• y = mx + b

• m is the slope (rate of change; rise/run)

• b is the y-intercept (starting value)

Multiple Choice

Identify the slope as positive, negative, zero or undefined.

• positive

• negative

• zero

• undefined

Multiple Choice

What is the y-intercept of this line: y = 2/3x - 4

• 2/3x

• 3

• 4

• -4

Multiple Choice

What is the slope of this line: y = 6x + 4

• y

• 4

• 6

• 1/6

Graphing using slope intercept form

• Plot the y-intercept on the y-axis

• Determine the slope

• Use the slope to move up (if the slope is positive) or down (if the slope is negative) from the point on the y-axis then to the right.

Multiple Choice

What is the y-intercept of this graph?

• (0,1)
• (0,-2)
• (0,0)
• (0,3)

Multiple Choice

Find the slope and y - intercept

y = 1/2x - 1

• slope: 1/2 y-intercept: -1

• slope: 2 y-intercept: -1

• slope: 1/2x y-intercept: 1

• slope: 2 y-intercept: 5

Multiple Choice

When you graph a line using slope-intercept form (y=mx+b), you graph the ___________ first and then use the ___________ to find the second point.

• origin; slope

• slope; y-intercept

• y-intercept; x-intercept

• y-intercept; slope

Multiple Choice

Which is the graph of y= -x + 2?

• A
• B
• C
• D

Writing Equations from graphs

• Identify the y-intercept (where the line crosses the y-axis)

• Determine the slope (rise/run - how you have to move to get from one point on the line to another)

• Plug in the slope for m, the y-intercept for b in y=mx+b

Multiple Choice

Write the equation for the line in slope-intercept form.

• y= -1x+3

• y= 4x+3

• y=1/4x+3

• y= -4x+3

Multiple Choice

Which equation matches the graph? (Click me to see the image)

• y = 2x

• y = 1/4 x + 2

• y = 1x + 4

• y = -2x

Multiple Choice

Write the equation of the line.

• y= -1x-3

• y= -3x-1

• y=-1/3x-1

• y= -3x-3

Writing equations from key information

• Always start with y = mx + b

• If you know the slope and y-intercept, plug in for m and b

• If you only know the slope and a point, plug in the slope and the x and y values to solve for b

Multiple Choice

How would you write the equation with a slope of 2/3 and a y-intercept of -3

• y=3/2x+3

• y=2/3-3

• y=2/3x-3

• y=2/3x+3

Multiple Choice

What is the equation of the line that has a slope of 5 and goes through the point (2,7)?

• y = 5x + 3

• y = 1/5x - 3

• y = 1/5x + 3

• y = 5x - 3

Multiple Choice

What is the equation of the line passing through points (1,1) and (3,-5).

• y = -3x + 4

• y = 3x - 4

• y = -3x - 4

• y = 3x + 4

Converting to slope-intercept form

• Step 1: distribute if you see parentheses

• Step 2: combine like terms

• Step 3: isolate y

• Step 4: write in the form y=mx+b

Multiple Choice

Write the following equation in slope intercept form:

y - 3 = -2(x + 4)

• y=2x-5

• y=-2x+7

• y=-2x-5

• y=-2x +1

Multiple Choice

What is the first step to convert this equation into slope-intercept form?
 $y+4=-9\left(x+3\right)$  

• Subtract 4 from both sides of the equation

• Add 4 to both sides of the equation

• Distribute -9 to everything in the parentheses

• Distribute 9 to everything in the parentheses

Multiple Choice

Which equation represents 4x - 2y = 6 in slope intercept form.

• y = 2x - 3

• y = -2x + 3

• 
  

  $y\ =\ \frac{1}{2}x\ -\ 3$

• y = 2x + 8

Linear vs. Non-linear

• Linear functions form a straight line and have a constant increase or decrease of y as x increases or decreases

• Non-linear functions do not form a straight line and as x increases, y does not increase at a constant rate

Multiple Choice

 $y\ =\ 6x\ +\ 5$  

• Linear

• Nonlinear

Multiple Choice

Linear or Nonlinear?

• Linear

• Non-Linear

Multiple Choice

Linear or Nonlinear?

• Linear

• Non-Linear

Multiple Choice

Linear or Nonlinear?

• Linear

• Non-Linear