Math 143 Week 3 Homework Worksheet
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School
University of Hawaii *
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Course
B370
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
4
Uploaded by CaptainKnowledge13128 on coursehero.com
Worksheet Assignment
Linear Regressions
Directions: These activity questions are written to follow the activity for
the week. After the weekly lecture class meetings, you should be able to
answer these questions. Answer the questions, save the document, and
submit the assignment to 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 the slope and the y-intercept. For
example, if the slope and y-intercept are given, you can simply write the
equation of the line. If you have a slope and one point but no y-intercept,
you can use the point-slope form (y – y1 = m(x -x1). With two points, you
can use slope-intercept form to create your line.
EX: If I had the points (0,4) and (4,8), I could calculate the slope by
determining the change between the two. I would do 0-4/4-8, which
would result in a slope of 1. My y-intercept is already included in one of
the points, therefore, my equation would be y=x+4.
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.
One is most likely to be given the information in observations. It’s pretty
rare for you to be given a random equation, however, it’s important that
we understand equations in case you need to apply them to get data
from other observations/data sets.
3.
What are the characteristics of linear data?
When you plot linear data points on a line, the points will resemble a
straight line (the data won’t always fit perfectly in a straight line). The data
of a linear equation typically has 1-2 variables as well!
4.
What is a line of best fit?
The line of best fit can be used when the data points on a graph don’t
form a perfectly straight line. This line is graphed with around half of the
data points above the line and half below. The line of best fit can help
give us an idea of where the data will continue to grow.
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).
We can use Y=MX+B to find this equation. Since we know that the slope
is (-2/3), we just need to figure out the y-intercept (B). We can solve this
by plugging (-1,6) into our equation and solving for B. This would give us
B=16/3. To rewrite this equation, we add our new B term, making the
equation Y=-2/3X+16/3.
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?
[3,24]
b) What is the range of the data?
[15.3, 43.2]
c) Create a scatterplot on your graphing calculator using
data. Sketch the scatterplot below.
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