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### Course: High school statistics>Unit 4

Lesson 2: Analyzing trend lines in scatterplots

# Equations of trend lines: Phone data

Paige collected data on how long she spent on her phone compared to how much battery life was remaining (in hours) throughout the day. Here is the data:
Time spent on phone (hours)$1$$2$$3.5$$4$$6$$7$$8$$9$
Battery life remaining (hours)$8$$7$$7$$5.5$$5$$3.5$$2.5$$2.5$
Now she wants a trend line to describe the relationship between how much time she spent on phone and the battery life remaining. She drew three possible trend lines:
problem 1
Which line fits the data graphed above?

problem 2
2) Which equation describes the best trend line above?

problem 3
Use the equation of the trend line to predict the battery life remaining after $3.6$ hours of phone use.
hours

problem 4
Use the trend line to predict the battery life remaining after $20$ hours of phone use.
hours

problem 5
Does the prediction from problem 4 seem reasonable in the context of the problem?

problem 6
What is the best interpretation of the slope of this trend line?

problem 7
What is the best interpretation of the $y$-intercept of this trend line?

Challenge problem
Paige wants to turn her phone off when the battery has $15$ minutes remaining, just in case she has an emergency and needs her phone later.
According to the trend line, how long can she spend on her phone before she needs to turn it off?
hours

## Want to join the conversation?

• How do you find the slope of the graph?
• Find two good points and count change in y (rise)/change in x (run)
• I do not understand how the last one is 11.7 I got 11.8?
• The trend line is 𝑦 = −0.75𝑥 + 9, where 𝑥 is the time spent on the phone (in hours) and 𝑦 is the expected battery life remaining (in hours).

Paige wants to turn her phone off when there's 15 minutes of battery life remaining.
15 minutes = 1∕4 hours ⇒ 𝑦 = 1∕4 = −0.75𝑥 + 9 ⇒
⇒ 𝑥 = (1∕4 − 9)∕(−0.75) = 11.6666... ≈ 11.7

So, Paige can use her phone for approximately 11.7 hours before she needs to turn it off.
• I don't get the rounding thing what do you have to round?
• Yes but I did the rounding and it was wrong. all the rounding did not work and i did exacts and i got them all right. if i rounded then it came up wrong.
• I still don't understand how to find the slope of a scatterplot when answers are not provided? How do you get the slope-intercept equation if the values are all over the place?
• You don't have to find the slope-intercept equation for the points. You need it for the trend line.
• i'm finding it hard to find the numbers that the line goes through. for example it says "the line goes through (0,9) and (4,6). where did these numbers comes from and how were they spotted. please help me with some steps or anything...
• The coordinates were on the purple line. If you look at the y-intercept, it is (0,9). If you go down to the next whole number point, it is (4,6).
• why was this insanely difficult for me? the estimating equations of lines took me an hour, and I didnt even get it done!
• How do you get 15 to be 1/4's?
• All our other values are in hours, so we would like to express 15 minutes in hours. Since there are 60 minutes in an hour, 15 minutes = 15/60 hours. Dividing top and bottom by 15 gives us 1/4.
• I am not sure I understand this right: if I do not use the phone at all I have 9 hours of battery left. If I then use it for 9 hours I still have circa 2 hours of battery left … ?

If beta (the thing in front of x) is smaller than one that would imply that the phone battery drains slower when in use then when in standby … that makes no sense!
• y slope actually and technically means not the actual remaining battery life but the "predicted" one based on usual usage patterns of a user by a manufacturer, I guess.

and the wording of left battery life made me confused too since this could imply a sort of futuristic ultra battery which may run infinitely as it always has an amount of battery left after an hour of usage, no matter how small it is!

if y slope was tagged as "expected battery life", it might give no confusion.