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# 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)123, point, 546789
Battery life remaining (hours)8775, point, 553, point, 52, point, 52, point, 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, point, 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?

• why was this insanely difficult for me? the estimating equations of lines took me an hour, and I didnt even get it done!
• 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 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.
• 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).
• its hard to find the answer to the last question i've been stuck on it for minuets
• Hi, where can I find the lesson that goes into details as to the maths behind the calculation done above? That is, if line goes thorugh (0,9) and (4,6), then the slope is equal to (6-0)/(4-9) = -0.75? How do we know which way to do the substitution?

My calculation would have been to say that we know that in y=ax+b, b has to be equal to 9 given that it's the intercept. From there, we know that 6 = 4a + 9, so we can derive that a = -0.75. But I want to learn the technique used above.
• From trigonometry, slope of the line is nothing but the height divided by base in a right angle triangle. So let say there are two points (0,9) and (4,6), imagine a right angle triangle created out these two points, now the base is (x2-x1) and height is (y2-y1) and hypotenuse the is line itself. Hence the slope will now be (y2-y1)/(x2-x1).
(1 vote)
• How do you get 15 to be 1/4's?