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 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 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'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).

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).

I don't understand trend lines or slope graphs. It is all too confusing.

Sometimes when i don't understand things I have to go back and revisit videos on the subject. https://www.khanacademy.org/math/algebra/two-var-linear-equations/slope/v/slope-of-a-line Go back over those and click on the videos of parts you do not understand. Hang in there, you will get it. :)

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.

Main content

Integrated math 1

Course: Integrated math 1 > Unit 9

Lesson 2: Estimating with trend lines

Equations of trend lines: Phone data

Google Classroom

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)	$8$ ‍	$7$ ‍	$7$ ‍	$5.5$ ‍	$5$ ‍	$3.5$ ‍	$2.5$ ‍	$2.5$ ‍

She then made this scatterplot:

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.
Round your answer to the nearest tenth of an hour.

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?

(Choice A)
For each additional $1$ ‍ hour of time spent on the phone, the predicted battery life remaining increases by $0.75$ ‍ hours.
(Choice B)
For each additional $1$ ‍ hour of time spent on the phone, the predicted battery life remaining decreases by $0.75$ ‍ hours.
(Choice C)
For each additional $0.75$ ‍ hours of time spent on the phone, the predicted battery life remaining decreases by $1$ ‍ hour.

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?
Round your answer to the nearest tenth of an hour.

hours

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CzerwonyG.21
Posted 7 years ago. Direct link to CzerwonyG.21's post “How do you find the slope...”
How do you find the slope of the graph?
Button navigates to signup pageComment on CzerwonyG.21's post “How do you find the slope...”
(18 votes)
Answer
- David Severin
  Posted 7 years ago. Direct link to David Severin's post “Find two good points and ...”
  Find two good points and count change in y (rise)/change in x (run)
  Button navigates to signup page
  (14 votes)
isabella.1988463
Posted 6 years ago. Direct link to isabella.1988463's post “I do not understand how t...”
I do not understand how the last one is 11.7 I got 11.8?
Button navigates to signup pageComment on isabella.1988463's post “I do not understand how t...”
(10 votes)
Answer
- Jerry Nilsson
  Posted 6 years ago. Direct link to Jerry Nilsson's post “The trend line is 𝑦 = −0...”
  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.
  Comment on Jerry Nilsson's post “The trend line is 𝑦 = −0...”
  (19 votes)
mike
Posted 6 years ago. Direct link to mike's post “I still don't understand ...”
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?
Button navigates to signup pageButton navigates to signup page
(10 votes)
Answer
- Karmanyaah Malhotra
  Posted 6 years ago. Direct link to Karmanyaah Malhotra's post “You don't have to find th...”
  You don't have to find the slope-intercept equation for the points. You need it for the trend line.
  Button navigates to signup page
  (4 votes)
Frenchy Starfire (I'm offiline so don't try anything funny XD)
Posted 7 years ago. Direct link to Frenchy Starfire (I'm offiline so don't try anything funny XD)'s post “I don't get the rounding ...”
I don't get the rounding thing what do you have to round?
Button navigates to signup pageButton navigates to signup page
(8 votes)
Answer
- huskybike
  Posted 7 years ago. Direct link to huskybike's post “Yes but I did the roundin...”
  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.
  Button navigates to signup page
  (7 votes)
unknown
Posted 7 years ago. Direct link to unknown's post “i'm finding it hard to fi...”
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...
Button navigates to signup pageButton navigates to signup page
(7 votes)
Answer
- vishib
  Posted 7 years ago. Direct link to vishib's post “The coordinates were on t...”
  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).
  Button navigates to signup page
  (5 votes)
jtouhill98
Posted 5 years ago. Direct link to jtouhill98's post “why was this insanely dif...”
why was this insanely difficult for me? the estimating equations of lines took me an hour, and I didnt even get it done!
Button navigates to signup pageButton navigates to signup page
(8 votes)
Answer
Jessica Velazquez
Posted 6 years ago. Direct link to Jessica Velazquez's post “How do you get 15 to be 1...”
How do you get 15 to be 1/4's?
Button navigates to signup pageComment on Jessica Velazquez's post “How do you get 15 to be 1...”
(4 votes)
Answer
- Rhulani
  Posted 5 years ago. Direct link to Rhulani's post “All our other values are ...”
  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.
  Button navigates to signup page
  (5 votes)
Lois Duhourcau
Posted 7 years ago. Direct link to Lois Duhourcau's post “Hi, where can I find the ...”
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.
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- Ashish Soni
  Posted a year ago. Direct link to Ashish Soni's post “From trigonometry, slope ...”
  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).
  Button navigates to signup page
  (2 votes)
Asma Karim Vallimohamed
Posted 6 years ago. Direct link to Asma Karim Vallimohamed's post “I don't understand trend ...”
I don't understand trend lines or slope graphs. It is all too confusing.
Button navigates to signup pageComment on Asma Karim Vallimohamed's post “I don't understand trend ...”
(5 votes)
Answer
- fr33d0g
  Posted 6 years ago. Direct link to fr33d0g's post “Sometimes when i don't un...”
  Sometimes when i don't understand things I have to go back and revisit videos on the subject.
  https://www.khanacademy.org/math/algebra/two-var-linear-equations/slope/v/slope-of-a-line Go back over those and click on the videos of parts you do not understand. Hang in there, you will get it. :)
  Comment on fr33d0g's post “Sometimes when i don't un...”
  (2 votes)
Paul Friedrich
Posted 5 years ago. Direct link to Paul Friedrich's post “I am not sure I understan...”
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!
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- deka
  Posted a year ago. Direct link to deka's post “y slope actually and tech...”
  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.
  Button navigates to signup page
  (5 votes)