Question

5. Which of the equations show x and y DIRECTLY proportional to each relationship? For every one that does provide the constant of proportionality

Answer 1

A direct proportional relation can always be express as an equation of the form:

`y=kx`

where k is the constant of proportionality. (This means that y has to be the result of multiplying a number by x)

Now, let's see at the option we have.

a)

Solving the equation for y we have:

`\begin{gathered} 2x+2y=0 \\ 2y=-2x \\ y=-(2)/(2)x \\ y=-x \end{gathered}`

Since we can write the equation in the form as a direct proportional relationship we conclude that option a shows a directly proportional relationship and that the constant is -1.

b)

For this case we have the equation:

`x=.125y`

From it we already can see that this means that x is directly proportional to y and that the constatn of porportionality is 0.125.

Now if we want we can solve the equation for y, then we have:

`\begin{gathered} y=(1)/(.125)x \\ y=8x \end{gathered}`

this equation shows that y is directly proportional to x and that the constant of proportionality is 8.

Notice that the the constant of proportionality changes if we write the relation as x directly proportional to y or if we write it as y directly proportional to x. Either way the relation express the same and it is directly proportional.

c) and d)

For this equations that we have a division in which one of the variables is the divisor (or the denominator); this means that the equation show a relation between x and y but their are not directly proportional. In fact this means that the equations show an inversely proportional relations.