The Slope of a Line
What makes a line different from other curves that are not lines?
How many lines contain both of the points Ð"ß  #Ñ and Ð%ß &Ñ?
What is the slope of a line that contains these two points?
Formula for the slope of a line:
If a line 6 contains the points with coordinates ÐB" ß C" Ñ and
C C
ÐB# ß C# Ñ, then the slope of the line 6 is given by 7 œ B"  B # or by
7œ
C2  C1
B2  B 1
"
#
Find the slope of the line that contains the points Ð#ß "# Ñ and
Ð  #$ ß %Ñ.
Find the slope of the line given by the equation #B  )C œ (
Find the slope of the line given by the equation
#C  $ œ  #ÐB  "Ñ
One of the important applications of slope is in calculating the average rate
of change of a dependent variable C with respect to a change in the
dependent variable B.
Example: In 1998 a company produced 2,300,000 computers for resale. In
2009 the same company produced 4,500,000 computers for resale. Use this
data to determine the average rate of change in the number of computers
produced per year by this company.
Example: When Jan was running a marathon she recorded the following
splits:
She finished mile 13 in 1.9 hours and she finished mile 20 in 2.8 hours. Use
this data to determine her average speed (rate of change in distance with
respect to time) between the 13 and 20 mile marks.
Use the slope formula to find the slope of the line that
contains the points Ð$ß #Ñ and Ð)ß #Ñ.
Use the slope formula to find the slope of a line that
contains the points Ð  #ß  %Ñ and Ð  #ß !Ñ.
The slope of a horizontal line is 0, and the slope of a
vertical line is undefined (a vertical line has no slope).
Parallel and Perpendicular Lines:
-Lines that are parallel have the same slope.
-Lines that are perpendicular have slopes that are opposite
reciprocals.
Find the slope of line 6 if line 6 contains the point Ð  "ß #Ñ
and is perpendicular to the line that contains the points
Ð$ß "# Ñ and Ð  "ß !Ñ.
Graph the line that contains the point Ð  #ß  $Ñ and has a slope
of 3.
Graph the line has a C-intercept of
$
#
and has a slope of  #& .