Resource Lesson
Properties of Lines
Printer Friendly Version
To calculate the
slope
,
m
, of a line passing through two points, (x
_{1}
, y
_{1}
) and (x
_{2}
, y
_{2}
) use this formula:
slope = Δy / Δx
slope = (y
_{2}
- y
_{1}
) / (x
_{2}
- x
_{1}
)
To calculate the line's
y-axis intercept
,
b
, use the formula,
y = mx + b
and substitute in the values of the slope,
m
, along with the coordinates of one data point - either (x
_{1}
, y
_{1}
) or (x
_{2}
, y
_{2}
). You can then solve for
b
, as it will be the only variable remaining in the equation.
The equation of the line can then be written as
y
=
m
x
+
b
once you substitute in your exact values for the line's slope and y-axis intercept.
Once you know the line's equation you can determine the coordinates of any of its other points.
Interpolation
means to use the equation of the line to determine the coordinate of a point that would fall inside the domain or range of the graph.
Extrapolation
means to use the equation of the line to determine the coordinate of a point that would fall outside the domain or range displayed on the graph.
Refer to the following information for the next ten questions.
A graph of Mass (grams) vs Volume (cm
^{3}
) for two samples composed of the same metal is linear. Two data points having the coordinates (2, 18) and (5, 42) have been plotted.
(1) Which variable belongs on the x-axis?
(2) State the coordinates of two grid-points that fall on this line.
(3) Solve for the numerical value of the slope?
(4) What are the dimensions (units of measurement) for this slope?
(5) What physical quantity is represented by the slope?
(6) Solve for the line's y-axis intercept.
(7) Does this value seem reasonable according to your graph? Explain?
(8) What is the equation of this line (please use correct variables: not x and y)?
(9) Interpolate a value for the mass present in a sample if its volume equals 3.5 cm
^{3}
.
(10) Extrapolate the volume required for a sample whose mass equals 100 grams.
Related Documents
Lab:
Labs -
2-Meter Stick Readings
Labs -
Acceleration Down an Inclined Plane
Labs -
Addition of Forces
Labs -
Circumference and Diameter
Labs -
Cookie Sale Problem
Labs -
Density of a Paper Clip
Labs -
Determining the Distance to the Moon
Labs -
Determining the Distance to the Sun
Labs -
Eratosthenes' Measure of the Earth's Circumference
Labs -
Force Table - Force Vectors in Equilibrium
Labs -
Home to School
Labs -
Indirect Measurements: Height by Measuring The Length of a Shadow
Labs -
Indirect Measures: Inscribed Circles
Labs -
Inertial Mass
Labs -
Introductory Simple Pendulums
Labs -
Lab: Rectangle Measurements
Labs -
Lab: Triangle Measurements
Labs -
Marble Tube Launcher
Labs -
Quantized Mass
Labs -
The Size of the Moon
Labs -
The Size of the Sun
Labs -
Video Lab: Falling Coffee Filters
Resource Lesson:
RL -
Basic Trigonometry
RL -
Basic Trigonometry Table
RL -
Curve Fitting Patterns
RL -
Dimensional Analysis
RL -
Linear Regression and Data Analysis Methods
RL -
Metric Prefixes, Scientific Notation, and Conversions
RL -
Metric System Definitions
RL -
Metric Units of Measurement
RL -
Potential Energy Functions
RL -
Properties of Vectors
RL -
Significant Figures and Scientific Notation
RL -
Vector Resultants: Average Velocity
RL -
Vectors and Scalars
Review:
REV -
Honors Review: Waves and Introductory Skills
REV -
Physics I Review: Waves and Introductory Skills
REV -
Test #1: APC Review Sheet
Worksheet:
APP -
Puppy Love
APP -
The Dognapping
APP -
The Pool Game
APP -
War Games
CP -
Inverse Square Relationships
CP -
Sailboats: A Vector Application
CP -
Satellites: Circular and Elliptical
CP -
Tensions and Equilibrium
CP -
Vectors and Components
CP -
Vectors and Resultants
CP -
Vectors and the Parallelogram Rule
WS -
Calculating Vector Resultants
WS -
Circumference vs Diameter Lab Review
WS -
Data Analysis #1
WS -
Data Analysis #2
WS -
Data Analysis #3
WS -
Data Analysis #4
WS -
Data Analysis #5
WS -
Data Analysis #6
WS -
Data Analysis #7
WS -
Data Analysis #8
WS -
Density of a Paper Clip Lab Review
WS -
Dimensional Analysis
WS -
Frames of Reference
WS -
Graphical Relationships and Curve Fitting
WS -
Indirect Measures
WS -
Lab Discussion: Inertial and Gravitational Mass
WS -
Mastery Review: Introductory Labs
WS -
Metric Conversions #1
WS -
Metric Conversions #2
WS -
Metric Conversions #3
WS -
Metric Conversions #4
WS -
Properties of Lines #1
WS -
Properties of Lines #2
WS -
Scientific Notation
WS -
Significant Figures and Scientific Notation
TB -
Working with Vectors
TB -
Working with Vectors
REV -
Math Pretest for Physics I
PhysicsLAB
Copyright © 1997-2020
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton