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Math
A |
Equations
of Straight
Lines |
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When working with straight lines,
there are many ways to arrive at an equation which represents the
line. |
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For information on graphing
straight lines, refer to Equations and
Graphs of Straight Lines.
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Information
about Slope |
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Slope is
always represented by the letter m when writing
equations of line.
Slope is found by using the formula:
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m
=
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Slope
is also
expressed as
rise/run.
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To
learn more about slope, refer to Straight
Lines and Slope . |
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Equation Forms
of Straight Lines |
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Slope Intercept Form
[if
you know the slope and the y-intercept (where the
line crosses the y-axis), use this form]
y=mx
+ b
m =
slope
b = y-intercept
(where line crosses the y-axis.) |
Point Slope Form
[if
you know a point and the slope,
use this form]
m = slope
 =
any point on the line
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Horizontal
Lines |
Vertical Lines |
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y = 3 (or
any number)
Lines that are horizontal
have a slope of zero. They have "run", but no
"rise". The rise/run formula for slope
always yields zero since
rise = 0.
y = mx + b
y = 0x + 3
y = 3
This equation also describes what is happening to the
y-coordinates on the line. In this case they are always 3. |
x = -2 (or
any number)
Lines that are vertical have no slope
(it does not exist). They have "rise", but no
"run". The rise/run formula for slope always has a
zero denominator and is undefined.
These lines are described by what
is happening to their x-coordinates. In this example, the
x-coordinates are always equal to -2. |
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Examples: |
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Examples
using Slope-Intercept Form: |
Examples
using Point-Slope Form: |
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1.
Find the slope and
y-intercept for the equation 2y = -6x + 8.
First solve for
"y =": y = -3x + 4
Remember the form: y = mx + b
Answer: the slope (m) is -3
the y-intercept (b) is 4
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3. Given that the slope of a line
is -3 and the line
passes through the point (-2,4), write the equation of the
line.
The slope: m = -3
The point (x1 ,y1) = (-2,4)
Remember the form: y - y1 = m ( x - x1)
y - 4 = -3 (x - (-2))
y - 4 = -3 ( x + 2) ANS.
If asked to express the answer in "y =" form:
y -4 = -3x - 6
y = -3x - 2
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2. Find
the equation
of the line whose slope is 4 and the coordinates of the
y-intercept are (0,2).
In this problem m = 4 and
b = 2.
Remember the form: y = mx + b
Substitute:
y = 4x + 2
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4. Find
the slope of the line that passes through the points (-3,5) and
(-5,-8).
Find
the slope:
Use either point: (-3,5)
Remember the form: y - y1 = m ( x - x1)
Substitute: y - 5 = 6.5 ( x - (-3))
y - 5 = 6.5 (x + 3) Ans.
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