Math A: 4.3
Since all lines have the same shape one of the important characteristics of a
line is how steep it is. We call this the slope of the line.
Definition 0.1 The slope of the line through the distinct points (x1, y1)and
(x2, y2)is
Slope =
Change in y
Change in x
=
Rise
Run
=
y2−y1
x2−x1
Draw the picture of the slope of a line.
Note that it does not matter which point you label (x1, y1) and which one you
label (x2, y2). But it is very important to stay consistent once the assignment
is made.
Example 0.1 Find the slope of the line passing through each pair of points.
•(3,1) and (5,4)
(x1, y1)and (x2, y2)
Slope =Change in y
Change in x =Rise
Run =y2−y1
x2−x1=4−1
5−3=3
2
•(2,5) and (3,5)
(x1, y1)and (x2, y2)
Slope =Change in y
Change in x =Rise
Run =y2−y1
x2−x1=5−5
3−2=0
1= 0
•(1,1) and (1,2)
(x1, y1)and (x2, y2)
Slope =Change in y
Change in x =Rise
Run =y2−y1
x2−x1=2−1
1−1=1
0=undefined
This line is not a function since it clearly fails the vertical line test.
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