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Linear Functions
A linear function in two variables is any equation of that may be written in the form
y = mx + b
where m and b are real number coefficients and x and y represent any real
numbers that make up a solution.
Furthermore, we observe that
•
The point (0, b) will always be the yintercept.
•
The slope of the line will always equal m.
•
The slope is defined as
m = (y
2
– y
1
)/(x
2
– x
1
)
for any two points on the line.
We call
y = mx + b the SlopeIntercept Form of the linear equation.
Slope
The slope of a line is defined descriptively as
the ratio of how far up you move divided by
how far to the right you move, as you move from one point to any other point on the line.
Example:
The graph of y = 2/3x – 1 has a slope of 2/3 and a yintercept of (0,1) as
shown below.
Negative Slope
If we must move down instead of up, a negative sign is part of the slope.
Also, if we
must move left instead of right, a negative sign is part of the slope. So if slope is
negative, we can interpret this in one of two ways:
•
m = (A/B) = (A)/B which would indicate that you move down A units and then right
B units.
•
m = (A/B) = A/(B) which would indicate that you move up A units and then left B
units.
Note that if we must move both down and left when moving from point to point, two
negative signs are incorporated into the slope and the result is a positive ratio.
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Example:
The graph of y = 2x +1 indicates a slope of –2. We may write m = 2 as
m = (2)/1.
So we move down 2 and right 1 when moving from point to point as shown
below.
Alternatively, we could write this slope as m = 2/(1) and move up 2 and left 1
when moving from point to point.
Example:
Calculate the slope of the line passing through (4,1) and (2, 2).
Then use
this slope to help graph this line.
The slope is given by
m = (y
2
– y
1
)/(x
2
– x
1
)
. So we substitute in our values to get
m =
2 – (1)
=
2 + 1
=
1
=
1
2 – 4
2
2
2
The graph is given by
From MathMotivation.com – Permission Granted For Use and Modification For NonProfit Purposes
Finding The Equation of a Line: The PointSlope Form
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This note was uploaded on 11/05/2011 for the course ANTHRO 101 taught by Professor Crandall during the Fall '09 term at BYU.
 Fall '09
 Crandall
 Anthropology

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