An Important Question of class 10 Based on Equation of a Straight Line Chapter of M.L Aggarwal for ICSE BOARD.
Here two parallel lines are given so you have find the value of p asked in question.
This is the Question Number 02, Exercise 12.2 of M.L Aggarwal.
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If 6x + 5y – 7 = 0 and 2px + 5y + 1 = 0 are parallel lines, find the value of p.
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For two lines to be parallel, their slopes must be same.
Given line equations,
6x + 5y – 7 = 0 and 2px + 5y + 1 = 0
In equation 6x + 5y – 7 = 0,
5y = -6x + 7
y = (-6/5) x + 7/5
So, the slope of the line (m1) = -6/5
Again, in equation 2px + 5y + 1 = 0
5y = -2px – 1
y = (-2p/5) x – 1/5
So, the slope of the line (m2) = -2p/5
For these two lines to be parallel
m1 = m2
-6/5 = -2p/5
p = (-6/5) x (-5/2)
Thus, p = 3