ZeePedia

Line and Definition of Slope

<< Coordinate Planes and Graphs
Distance, Circles, Quadratic Equations >>
img
Calculus and Analytical Geometry
MTH101
LECTUER ­ 4
Line and Definition of Slope
horizontally
Consider a particle moving along a
non vertical line segment from a point
p1( x1,y1 ) to a point p1( x1,y1 )  .
The vertical change y2 ­ y1 is called
the rise, and the horizontal change
Example: In each part find the slope of
x2 ­ x1the run.
the line through
Solution:
We know that slope of line through two points
p1( x1,y1 ) and p1( x1,y1 ) , is given by
m= y2 ­ y1
x2 ­ x1
So
On coordinate plane xy
Similarly
Mth101
Page 11
img
Calculus and Analytical Geometry
Line and Definition of Slope
On coordinate plane xy
Also
On coordinate plane xy
If m is slope of line then,
For a
line L is
Example:
As shown in the following figures.
Solution:
Mth101
Page 12
img
Calculus and Analytical Geometry
Line and Definition of Slope
The proof of the converse is left as an
exercise.
Proof:
(a)
If L1  and L2  are non vertical lines, then their
angles of inclination Ø1 and Ø2   are equal.
Thus
Conversely, if two slope lines are equal, I.e.
M1 = M2
tan(Ø1)=tan(Ø2)
Ø1 = Ø2
So, lines are parallel.
(b) Assume that
Then referring to the figure
Mth101
Page 13