Question

Write the direct linear variation equation for the relationship: y varies directly with x and y = 4 when x = 12.

Answer 1

The direct linear variation equation relationship statement is y varies directly with x. Therefore:

y α x

To change it to an equality, we insert k as the constant of proportionality.

y = kx

At y = 4, x = 12

4 = k(12)
k = 1/3

Therefore, the equation is:

y = (1/3)x

Answer 2

y
`\alpha x`
y=kx
where k is a constant of proportionality;
if y=4, x=12
4=12k
k=4/12
k=1/3
y=
`(1)/(3) x`