Q3) Find the equation of the line which passes through the point of intersection of
lines x+2y+6=0, 2x - y = 2 and which makes intercept 5 on the Y-axis.
Answers
Step-by-step explanation:
Given :-
The lines x+2y+6=0
2x - y = 2
To find :-
Find the equation of the line which passes through the point of intersection of
lines x+2y+6=0, 2x - y = 2 and which makes intercept 5 on the Y-axis. ?
Solution :-
Given lines are x+2y+6 = 0 ---------(1)
and 2x-y = 2 ----------(2)
=> 2x-2 = y ------------(3)
On Substituting the value of y in (1) then
=> x + 2(2x-2) +6 = 0
=> x +4x-4+6 = 0
=> 5x+2 = 0
=> 5x = -2
=> x = -2/5
On Substituting the value of x in (3) then
=> y = 2(-2/5)-2
=> y = (-4/5)-2
=> y = (-4-10)/5
=> y = -14/5
The solution = (-2/5 , -14/5)
The solution is the point of intersection of the two lines .
And
Given that Intercept of y-axis = 5
We know that
The general form of the line with slope and y - intersept is y = mx+c
=> -14/5 = m (-2/5) + 5
=> -14/5 = (-2m+25)/5
=> -14 = -2m+25
=> -14-25 = -2m
=> -39 = -2m
=> -2m = -39
=> 2m = 39
=> m = 39/2
The slope = 39/2
Now the required equation of the line
=> y = (39/2)x+5
=> y = (39x+10)/2
=> 2y = 39x+10
=> 39x-2y+10 = 0
Answer :-
The required equation of the line for the given problem is 39x-2y+10 = 0
Used formulae:-
→ The general form of the line with slope and y - intersept is y = mx+c
Used Method :-
→ Substitution method