Lecture no.1 Part 2

Lecture no.1 Part 2
Rectangular coordinate system or Cartesian coordinate in the plane :

Point in the plane can be identified with ordered pairs of real numbers, to begin we draw two perpendicular coordinate lines that intersect at the o-point of each line , these line are called coordinate axes in the plane .

y


3

2
P(1,1)
1 .
-3 -2 -1 1 2 3 x


-1
Q(-2,-2)
-2

-3


Slope : any non vertical line in the plane has the property that the ratio :

M=

Has the same value for every choice of the two points on the line , note that
The angle of inclination of a line horizontal is zero, for vertical line is 90, if we expressed the angle of inclination by then .
The relation between the slop m and inclination line is :

M=
The equation of nonvertical straight line with slope m
M= y-y1/x-x1
Y=y1+m(x-x1)

Example : write an equation of the line that passes (2,3) with slope -3/2

Y=3-3/2(x-2)= 3- 3/2 x+6/2
When x=0 then y=6
Y=0 then x=4


Example : write the equation of the line passing through (-2,-1), (3,4)


Slope= (-1-4)/(-2-3)=1 or y=4+1(x-3)
Y=-1+1(x-(-2)) =4+x-3
Y=x+1 y= x+1