Lecture Note Function
The Slope of a Line
The slope of the nonvertical line passing thruough the points
()xy 11 , and ( )x2 2,y is given by the formula
21
21
Slope
y yy
x xx
Δ −
==
Δ −
y
Example 1
Find the slope of the line joining the points(−2, 5 and 3, 1) ( − ).
3.2 Horizontal and Vertical Lines ...................................................................
The horizontal line has the equationyb= , where b is a constant. Its
slope is equal to zero. The vertical line has the equationx=c, where
c is a constant. Its slope is undefined. See the figure.
3.3 The Slope-Intercept Form .........................................................................
The Slope-Intercept Form of the Equation of a Line
The equation
ymxb= +
is the equation of the line whose slope is m and whose y intercept
is the point()0,b
Example 2
Find the slope and y intercept of the line 32 yx+ = 6 and draw the graph.
3.4 The Point-Slope Form ...............................................................................
The Point-Slope Form of the Equaiton of a Line
The equation yy−= − 00 mx x( )is and equation of the line that
passes through the point (xy 00 , )and that slope equal to m.
Example 3
Find an equation of the line that passes through the point (5,1)and
whose slope is equal to1/2.
Example 4
Find an equation of the line that passes through the points(3, 2 and 1, 6− )().
•
•
(x 22 ,y)
( ) yy y^21 −
11 ,
=Δ
21
x y
x−xx=Δ
x
y
y x=c
- x
(0,b) yb=
Horizontal line
(c,0)• x
Vertical line