| Slope |
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Slope - The slope m of a line is the RATIO of the change in the y-coordinates to the corresponding change in the x-coordinates of ANY TWO POINTS on the line.
Determining Slope
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N.B. Henceforth, please read x1 as "x sub 1" and y2 as "y sub 2" and so on |
Given the
coordinates of ANY two points,
(x1 ,
y1 )
and (x2 ,
y2 ),
on a line, the slope m can be calculated
by:
For the points ( 1, 0 ) and ( 3 , 4 ):
For the points ( -2, 5 ) and ( 6 , 1 ):
N.B. Please note that either ordered pair can be subtracted from the other and the same slope result will be derived. In other words, it doesn't matter which point is designated as (x1 , y1 ) or (x2 , y2 ).
Do Now: Calculate the slope for each of the following sets of ordered pairs:
a) ( 3, 4 ) , ( 4, 7 )
b) (-5, 6 ) , (-3, 8 )
c) (-5, 6 ) , (-2, 3 )
d) ( 2, -4 ) , (-2, 8 )
e) ( 0, 0 ) , ( 6, 2 )
f) (-6, -2 ) , (12, 4 )