Download slope

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§ 2.3 Slope of a Line
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Slope
 Definition: The slope of a line passing
through the points 𝑥1 , 𝑦1 , 𝑥2 , 𝑦2 is
𝑦2 − 𝑦1
𝑚=
𝑥2 − 𝑥1
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Examples:
𝑦2 − 𝑦1
𝑚=
𝑥2 − 𝑥1
1.) (-5,-1),(8,2)
2.) (6,-9),(6,-3)
3.) (-4,-7),(5,-7)
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More About Slope
 In words, the slope is the change in y divided by
the change in x.
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More About Slope
 In words, the slope is the change in y divided by
the change in x.
 Sometimes written as,
Δ𝑦 𝑦2 − 𝑦1
𝑚=
=
Δ𝑥 𝑥2 − 𝑥1
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More About Slope
 In words, the slope is the change in y divided by
the change in x.
 Sometimes written as,
Δ𝑦 𝑦2 − 𝑦1
𝑚=
=
Δ𝑥 𝑥2 − 𝑥1
𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒
"𝑟𝑖𝑠𝑒" 𝑜𝑟 "𝑓𝑎𝑙𝑙"
𝑚=
=
ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 "run" (𝑙𝑒𝑓𝑡 𝑡𝑜 𝑟𝑖𝑔ℎ𝑡)
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Finding the slope of a line given the
Graph
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Slopes of Horizontal and Vertical
Lines
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Slopes of Horizontal and Vertical
Lines
 Equations of the form y = b (where b is a
number) have slope equal to 0.
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Slopes of Horizontal and Vertical
Lines
 Equations of the form y = b (where b is a
number) have slope equal to 0.
 Equations of the form x = a (where a is a
number) have no defined slope.
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Slope of Parallel Lines
 Parallel lines have the same slope. Also, two
lines with the same slope are parallel.
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Slopes of Perpendicular Lines
 Two lines are perpendicular, if their slopes
are negative reciprocals of each other.
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Remember
A line by itself is not parallel. A line has to be
parallel to another line. Same goes for
perpendicular lines.
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Negative Reciprocals
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Negative Reciprocals
 The negative of a number is just the same
number with opposite signs.
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Negative Reciprocals
 The negative of a number is just the same
number with opposite signs.
 The negative of 3 is just -3.
 The negative of
7
−
11
is just
7
.
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Negative Reciprocals
 The negative of a number is just the same
number with opposite signs.
 The negative of 3 is just -3.
 The negative of
7
−
11
is just
7
.
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 The reciprocal of a number is just the number
“flipped around”.
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Negative Reciprocals
 The negative of a number is just the same
number with opposite signs.
 The negative of 3 is just -3.
 The negative of
7
−
11
is just
7
.
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 The reciprocal of a number is just the number
“flipped around”.
 The reciprocal of 3 is just
 The reciprocal of
7
−
11
1
.
3
is just
11
− .
7
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What is the negative reciprocal of
the following numbers?
 1.)
3
4
 2.) −5
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Examples
Determine whether the line that passes through
the two points is parallel, perpendicular, or
neither to a line with slope of -2.
1.) −2, −6 , 3,4
2.) 2,7 , −2,5
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FYI Note
If when you multiply the slopes of two lies
and you get -1, then they are perpendicular.
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Final Note
Are the lines, 𝑥 = 3 and 𝑦 = 5,
parallel, perpendicular, or neither to each
other?