Consider the complete question is "The equation of the line
is y=5x+1 and the equation of line
is 2y-10x+3=0. How can you show that these two lines are parallel?"
Given:
Equation of
is
.
Equation of
is
.
To show:
The these line as parallel.
Solution:
We have,
...(i)
...(ii)
Equation (ii) can be written as
...(iii)
Slope intercept form of a line is
...(iv)
where, m is slope and b is y-intercept.
On comparing (i) with (iv), we get slope of line
.
On comparing (iii) with (iv), we get slope of line
.
Since,
, therefore, lines
and
and parallel because slope of two parallel lines are always equal.
Hence proved.