Math 143 Week 3 Desmos 2022 Activity Worksheet
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School
Boise State University *
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Course
143
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
4
Uploaded by AgentCrownDove34
M143 Week 3 Worksheet Math 143 Week 3 Activity Worksheet Linear Regressions Directions: These activity questions are written to follow the Desmos activity for the week. Once you have completed the weekly activity you will be able to answer these questions. You can complete the questions on any document and then hand in the document on Canvas. 1.
What information is required to find the equation of a line? Give an example, then use your explanation to find the equation of your line. To find the equation of a line, you need to know two things: how steep the line is (its slope) and at least one point it goes through. For example, if I tell you a line goes up by 2 every time it moves to the right by 1 and that it passes through the point (3, 5), you can figure out its equation. 2.
When working with numerical information outside the math classroom, one is most likely to be given the information in what form? Mathematical Equations? Data Sets? Observations? Explain. In your field of study give an example. When you're dealing with numbers in real life, like counting things or measuring stuff, you usually get them as sets of data, not as fancy math equations. For instance, if you're studying language like I do, you might get a bunch of sentences to analyze, not a bunch of complicated math equations. 3.
What are the characteristics of linear data? Linear data means when you graph it, the points make a straight line, not a curve. If you increase one thing by the same amount, the other thing increases by a steady amount too. It's like climbing stairs where each step is the same height. 4.
What is a line of best fit? A line of best fit is like drawing a line through a bunch of points on a graph to show the general trend. It helps us see where the data is headed and make predictions.
M143 Week 3 Worksheet 5.
Given the slope and a point that a line passes through, explain how you can find the equation of the line. Find the equation of a line with a slope of -2/3 and passes through the point (-1, 6). If I give you the slope (how steep the line is) and one point the line goes through, you can find the equation of the line. For example, if a line goes down 2 for every 3 it moves to the right and it goes through the point (-1, 6), you can use those numbers to figure out the equation of the line. 6.
A student is hanging masses from a spring and measuring the resulting stretch in the spring. The following table shows the students’ collected data.
m
(mass in grams) 3 7 9 16 24 x (stretch in cm) 15.3 21.0 25.1 33.4 43.2 a)
What is the domain of the data? The domain is all the different inputs you have, like the different masses of the weights. In this case, it's {3, 7, 9, 16, 24}. b)
What is the range of the data? The range is all the different outputs you get, like how much the spring stretches. In this case, it's {15.3, 21.0, 25.1, 33.4, 43.2}. c)
What strategy would you use to find the resulting stretch of the spring if a mass of 20 g were placed on the spring? Be descriptive in your explanation of the strategy. To find out how much the spring stretches with a weight of 20 grams, you'd look at the closest weights you have data for and make a guess based on them. d)
Plot the data using Desmos. Sketch the plotted data below. Make sure to label the axis on your graph.
M143 Week 3 Worksheet e)
What window did you use on Desmos? Explain why you chose this window. I set up the graph so I can see all the points clearly without leaving too much empty space. f)
What type of curve would best fit the data? Linear? Quadratic? Cubic? Exponential? Justify your choice. Based on the data, it looks like a straight line would fit best because the points seem to follow a straight pattern. g)
Could you create a linear regression equation by hand of this data? Explain. Yes, you can figure out a line that fits the data by doing some math with the points you have. h)
Is the Desmos regression or the by hand regression more accurate? Explain. Usually, the computer's line fitting is better because it considers all the points accurately. Doing it by hand might have mistakes. i)
Using Desmos, calculate the linear regression that best fits your data. Write your equation below. x=0.7925m+17.05
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M143 Week 3 Worksheet j)
Explain a situation where you would use this regression equation. You might use this equation to guess how much the spring would stretch for a weight you haven't tried yet k)
How far would the spring stretch if the mass was 20 g? 16.85 cm 7) How many hours do you need to spend on Aleks actively working each week? 5 hours