Question

let y vary directly as x. if y=8 & x=2, then write a linear equation. what is the value of y when x =6

Answer 1

when y vary directly as x
Then ,
y≈x

y=kx
where k is the proportionality constant.

when y=8, x=2
8=2k  => k=4

so

Linear Equation is y=4x

when x=6, y=24

Answer 2

The answer is given below :

Since, y varies directly to x, we can write

y ∝ x

So,

y = kx, .....(i)
where k is any variation constant ≠ 0

Now, we need to find the value of k.

When y = 8 and x = 2, from (i) no. equation, we get

8 = k × 2

⇒ k = 8/2

⇒ k = 4

Now, for k = 4, from (i), we get a linear equation

y = 4x .....(ii)

Now, we need to find the value of y when x = 6.

Putting x = 6 in (ii) no. equation, we get

y = 4 × 6

⇒ y = 24

Therefore, we conclude that when x = 6, the value of y be y = 24.

LINEAR EQUATION :

An equation of one degree is called a linear equation because it represents a straight line in two dimension.
E.g., ax + by + c = 0 is a linear equation.

Thank you for your question.