Question

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

x y
4 6.4
7 11.2
10 16
13 20.8

Answer 1

If y is directly proportional to x , y should increase with a constant value when x is increasing with a constant value and vice and versa...
hence the two values r keep increasing by constant values

here x is getting increased by +3 each time and y keeps increasing by +4.8 as x increases
therefor we can say y varies directly with x.

hence x and y keep increasing from constant values we can say...
y = kx
and
k = y/x
= 6.4/4

therefor ....
y =(6.4/4)x
= (1.6)x
multiply both sides by 10
10 y = 16x