Explain how you can tell if a function is a linear based on its equation

If a function is linear, that means the degree on the x variable is 1 when solved for y. This means that the exponent on the x is 1. For example:

y²=x
y=√x
y=x^1/2

This is not a linear function because the power on the x function is not 1

x+y=3
y=-x+3

This is a linear function because the exponent on the x is 1.

Any function where the x doesn't have an exponent present, or has an exponent of 1, is deemed a linear function. 

Larger rocket: 36 kiloliters

smaller rocket: 24 kiloliters

Step-by-step explanation:

Lets assign the letters: "L" to the number of kiloliters the "Larger" rocket gets, and "S" to the number of kiloliters that the "Smaller" rocket gets.

We can create two equations from the words given in the problem:

First equation: A total of 60 kiloliters is to be used for "L" plus "S":

which gives us:

Next equation comes from the words: "The smaller rocket receives 12 kiloliters less than the larger rocket"

which gives us:

Now we can use this last equation to replace for the "S" unknown in the first equation (and thus reducing the problem to one equation with one unknown (L), that one can easily solve):

Therefore the amount of fuel that the larger rocket gets is 36 kiloliters.

And using the equation  "S = L - 12" we get:

Which tells us that the smaller rocket gets 24 kiloliters of fuel.