Unformatted text preview: hat slope can be described as the
ratio ‘ rise ’. For example, in the second part of Example 2.1.1, we found the slope to be 1 . We can
run
2
interpret this as a rise of 1 unit upward for every 2 units to the right we travel along the line, as
shown below.
y
4
‘up 1’
3
‘over 2’
2
1 −1 2 1 2 3 x Some authors use the unfortunate moniker ‘no slope’ when a slope is undeﬁned. It’s easy to confuse the notions
of ‘no slope’ with ‘slope of 0’. For this reason, we will describe slopes of vertical lines as ‘undeﬁned’. 114 Linear and Quadratic Functions Using more formal notation, given points (x0 , y0 ) and (x1 , y1 ), we use the Greek letter delta ‘∆’ to
write ∆y = y1 − y0 and ∆x = x1 − x0 . In most scientiﬁc circles, the symbol ∆ means ‘change in’.
Hence, we may write
∆y
,
∆x
which describes the slope as the rate of change of y with respect to x. Rates of change abound
in the ‘real world,’ as the next example illustrates.
m= Example 2.1.2. At 6 AM, i...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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