Give the equations of two lines passing through (3, 12). How many more such lines are there, and why?
Answers
Equation of two lines are
1) y-4x=0
2) x+y=15
Infinite number of lines can pass through one point.
for x=3 & y=12
1) In y-4x=0
putting y=12 &x=3
12-4(3)=12-12=0
this means y -4x passes from (3,12)
2) In x+y=15
putting y=12 &x=3
3+12=15
this means x + y = 15 passes from (3,12)
Now , from a given point infinite no. of lines can pass as we can make as much equation as we want.
y = 12 , y = x + 9 , y = 2x + 6 , y = 3x + 3 . y = 4x , x = 3 are few equations of lines passing through (3, 12)
Step-by-step explanation:
infinit lines can be drawn from a given points
one line can be drawn for given two points
Equation of line
y = mx + c
m can take any value
c will depend upon value of x & y of given point
m = 0
=> 12 = 0 * 3 + c
=> c = 12
y = 12
m = 1
=> 12 = 1 * 3 + c
=> c = 9
y = x + 9
m = 2
=> 12 = 2 * 3 + c
=> c = 6
y = 2x + 6
m = 3
=> 12 = 3 * 3 + c
=> c = 3
y = 3x + 3
m = 4
=> 12 = 4 * 3 + c
=> c = 0
y = 4x
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