Question

For each equation, determine whether it shows a direct variation (that is, shows directly proportional variables) If it does, find the constant of variation and write it in simplest form. 5y = 10x Direct variationk=Not direct variation -2x = 3y - 8 Direct variation k= Not direct variation

Answer 1

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx

where

k is the constant of proportionality

so

Part 1

we have

5y=10x

isolate the variable y

y=(10/5)x

y=2x

this equation is of the form y=kx

therefore

represent a direct variation

the value of k is 2

Part 2

we have

-2x = 3y - 8

isolate the variable y

3y=-2x+8

y=-(2/3)x+8/3

this equation is not of the form y=kx

therefore

Not direct variation​