find the slope ratio? using the rule?maestrodeyo.weebly.com/uploads/1/7/1/0/17102056/im_8__ch...c) Draw a line of best fit for the data. Find the equation of the line of best fit

IM 8 Ch 7.3.1 How Can I Use An Equation

CPM Materials modified by Mr. Deyo

Common Core Standard: 8.SP.3

What is being compared to find the slope ratio?

Can I make a prediction using the rule?


By the end of the period, I will write the equation for a line of best fit to represent scattered data that is roughly linear by calculating the slope from two points.

I will demonstrate this by completing Four‑Square notes and by solving problems in a pair/group activity.

Learning TargetTitle: IM8 ‑ Ch. 7.3.1 How Can I Use an Equation? Date:


Home Work: Sec. 7.3.1Desc. Date Due

Review & Preview

3 Problems: 7‑92, 7‑94, 7‑95



Vocabulary1) Scatterplot

2) slope

3) yintercept

4) y = mx + b



7.3.1 How Can I Use an Equation?Previously, you have learned to find and extend patterns in data and to make predictions using rules, equations, and graphs. Today you will apply these mathematical tools to a real situation in which your data does not make a perfect pattern. As you work with your study team today, keep the following questions in mind:

What is being compared to find the slope ratio?

Can I make a prediction using the equation?


787. AURÉLIE’S BIKE RIDE To prepare for a 30mile ride for charity, Aurélie has been biking every weekend. To predict how long the charity event will take her to complete, Aurélie has been keeping track of her time and distances. She tries to ride at a constant pace, but of course that is not easy to do. a) Would a box plot, scatterplot, or histogram be most useful in helping Aurélie make a prediction?

b) Considering that Aurélie is trying to predict how long it will take to complete the ride, which is the independent variable and which is the dependent variable? Make a scatterplot.

c) Use a line of best fit to predict how long it will take Aurélie to complete the charity ride. Remember that the line does not need to intersect each of the points and that the line does not need to pass through the origin to model the data.

Distance (miles)

TIme (m

inutes)


788. USING AN EQUATION TO MAKE PREDICTIONS Sometimes it is more convenient and more accurate to use an equation to make a prediction rather than making a prediction by reading a graph.

a) From 787, choose two points that lie on your line of best fit. These points can be given data points or lattice points on the coordinate grid. Use these two points to calculate the slope of your line of best fit. What does the slope mean in terms of Aurélie’s bike riding?

b) What is the y‑intercept of your line of best fit? What does the y‑intercept mean in terms of Aurélie’s training?

d) Use your equation to predict how long the 30 mile charity ride would take Aurélie to complete. How did your prediction compare to the prediction you made from the graph in part (c) of problem 787? y = ( )x + ( )

c) Write the equation of the line of best fit in y = mx + b form. Identify your variables.


789. Westland Workers Union’s Health and Wellness Department started a voluntary lunchtime running club. Members kept track of how much they ran each week for exercise and how much their resting heart rate dropped over several weeks. Their data is in the table at right. Note that a negative heart rate change is actually a gain in heart rate.

a) Make a scatterplot of the data. b) Describe the association.

c) Draw a line of best fit for the data. Find the equation of the line of best fit.

y = ( )x + ( )d) Use the equation to predict the heart rate change for an employee who ran 10 miles a week.

e) Interpret the slope and y‑intercept in this situation.


In your Learning Log, describe how to find the equation of a line in y = mx + b form from a graph of points. Include an example of how to calculate the slope from two points.

790. LEARNING LOG “Line From Data Points” Date ________


791. Anthony has added a line of best fit to the scatterplot here. Do you agree with where he put the line? Explain your reasoning.

http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch7/lesson/7.3.1/problem/791

http://homework.cpm.org/cpm-homework/homework/category/CC/textbook/CC3/chapter/Ch7/lesson/7.3.1/problem/7-91


792. Graph y = −1 x + 6. Find its x‑ and y‑intercepts. 2

a) Where's the xintercept?

Graph

b) Where's the yintercept?

( , )


( , )



793. Graph a line that goes through the points (0, 3) and (2, −1).

a) What is the slope of the line?Graph

b) Where's the yintercept?

( , )


c) What is the rule?

y = ( )x + ( )



794. How many yearbooks should your school order? Your student government surveyed three homeroom classes, and 55 of 90 students said that they would definitely buy a yearbook. If your school has 2000 students, approximately how many books should be ordered? Show and organize your work.

Our school should order __________ books.




795a. Find the perimeter and area of each triangle. http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch7/lesson/7.3.1/problem/795

Perimeter Area



795b. Find the perimeter and area of each triangle. http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch7/lesson/7.3.1/problem/795

Perimeter Area



796. Graph the lines y = −4x − 3 and y = −4x + 1 a) Where do they intersect?Graph

b) Solve this system using the Equal Values Method.

c) Explain how your graph and algebraic solution relate to each other.

https://www.desmos.com/calculator/yhbsc8xi3chttp://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch7/lesson/7.3.1/problem/796

( , )

4x 3 = 4x + 1

https://www.desmos.com/calculator/yhbsc8xi3c


Documents

find the slope ratio? using the rule?maestrodeyo.weebly.com/uploads/1/7/1/0/17102056/im_8__ch...c) Draw a line of best fit for the data. Find the equation of the line of best fit