Answer:
The equation of line passing through origin and parallel to first line is 5 X + 3 Y = 0
Step-by-step explanation:
Given as :
The points through which line AB passes are A ( - 3 , 0) and B ( -6 , 5 )
SO the slope line AB = (m1) = [tex]\frac{y2 -y1}{x2 - x1}[/tex]
Or, (m1) = [tex]\frac{5 - 0}{-6+3}[/tex]
Or, (m1) = [tex]\frac{5}{-3}[/tex]
Now Another line passes through origin ( 0 , 0)
And another line is parallel to first line AB , so, (m2) = (m1 ) = [tex]\frac{5}{-3}[/tex]
Now equation of another line passing through origin and slop (m2) is :
Or, Y - 0 = [tex]\frac{5}{-3}[/tex] (X -0)
Or - 3 Y = 5 X
∴ Y = - [tex]\frac{5}{3}[/tex] X
Hence The equation of line passing through origin and parallel to first line is 5 X + 3 Y = 0 Answer
