# Quarantine Question #2 Homeschool Detention: Linear Relationships and Lines of Best Fit

Find solutions linked here.

#### Grade 6-8 should be able to complete parts A and B of both problems.Grade 7-8 should be able to complete all of question 1 and parts A through D on problem 2.Grade 8 should be able to complete all parts.I encourage students of any grade to challenge themselves to work as far as they can using the resources linked below.

1. Mr. Kissner has given less detention in the last two weeks than at any time in his teaching career!  Either his students have become much better behaved, Mr. Kissner has gotten a lot more patient, or his students haven't been coming to school...  Some students, however, were assigned detention at home by their parental units during this trying time.  Farrick, a good natured child with a penchant for talking and goofing around, earned "detention" every day from his mom.  The number of minutes he earned each day is as follows:  A.  Complete the table.

B.  Graph the amount of detention Farrick earned by day.  (Video: graphing data from a table)

C. What is the rate of increase in detention per day?

D. What is the equation that models the amount of detention that Farrick earns each day?  (Video: Find equation from table of valuesPractice Problems. Video: Find equation from a graph, practice problems and solutions)

E.  Make a prediction based on your models:  If the homeschool-quarantine lasts for several more weeks, how many minutes of detention will Farrick have on day 20?  On day 100?

F.  What would be a possible explanation for Farrick's detention increasing daily?

2.  Hadyn also earns a substantial amount of at-home "detention" during this time.  The number of minutes he earned each day is as follows: A.  Graph, by hand, the amount of detention Hadyn earned by day.

B.  Draw a line of best fit through the data points.  (Video: Finding the line of best fit and the equation)

C.  Find an equation that models the relationship between minutes of detention earned and day of homeschool-quarantine.

D.  Use your equation to predict the number of minutes of detention Hadyn will earn on day 20 and day 100.

E.  Use google sheets or excel to graph the data and find the equation of the line of best fit that models the relationship. (Video: Using google sheets to create a scatterplot and line of best fit)

F.  Use your computer generated equation to predict the number of minutes of detention Hadyn will earn on day 20 and day 100.

G.  Describe similarities and differences between your hand-drawn and computer-generated graphs and equations.