If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Integrated math 1

### Course: Integrated math 1>Unit 9

Lesson 2: Estimating with trend lines

# 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$
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?

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

## 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 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).
• 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.
• 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).