Question

Give the equation of two lines passing through ( 2, 14). How many more such lines are there and why?

Answer 1

Answer:

Solution :

Let , The equation is

⇒x + y = k

⇒(x , y) = (2 , 14)

⇒2 + 14 = 16k

⇒16 = k

x + y = 16

⇒2x + 3y = k

⇒2(2) + 3(14) = k

⇒4 + 42 = k

⇒46 = k

2x + 3y = 46

⇒x -y = k

⇒2 - 14 = k

⇒k = -12

x - y = -12

⇒7x - y = k

⇒7(2) - 14 = k

⇒14 - 14 = 0

⇒k = 0

7x - y = 0

Therefore , We can write infinitely many such lines bacause infinitely many lines can be drawn to pàss through a point.