SOLUTION: Can you help me with the following problem? The solutions of line "a" are (3,3) and (5,5). The solutions of line "b" are (3,-3) and (5,-5). a. Form the equations of both th

Question 131018: Can you help me with the following problem?
The solutions of line "a" are (3,3) and (5,5).
The solutions of line "b" are (3,-3) and (5,-5).
a. Form the equations of both the lines.
b. What are the co-ordinates of the point of intersection of lines a and b?
Answer by pug912(10) (Show Source): You can put this solution on YOUR website!
for line a, first you need to find out the slope of line a.
slope of line a = (5-3)/(5-3) = 2/2=1 = m
use line equation y -y1 = m(x-x1) where (x1,y1) is either your (3,3) or (5,5).
so the equation of line a is:
y-3 = 1*(x-3)
y-3 = x-3
y = x --> line a
for line b, first you need to find out the slope of line b.
slope of line a = (-5+3)/(5-3) = -2/2= -1 = m
use line equation y -y1 = m(x-x1) where (x1,y1) is either your (3,-3) or (5,-5).
so the equation of line a is:
y+3 = -1*(x-3)
y+3 = -x+3
y = -x --> line b
now, to find out the intersection point of these two lines.
y=x (line a) and y=-x (line b)
subtitute y=x into equation of line b,
so we have y = -y , Hence, y=0.
now subtitude y=0 to equation of line a . we have x=0
so (0,0) is the intersection point of line a and b.
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