Does the chart below represent a proportional relationship? What is the rate of change?
1 answer:
This chart represents a proportional relationship. The rate of change will be 4.
<h3>What is the constant of proportionality?</h3>Firstly, there is a proportional relationship.
Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.
The constant k is called the constant of proportionality.
Given;
x y
1 4
2 8
3 12
4 16
Here, x = ky
put the first value
k = 1/4
This chart represents a proportional relationship.
So the rate of change will be
Learn more about proportional ;
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Here's how you simplify those. The rule for raising an exponent to an exponent is that you multiply them. The rule for dividing exponents with the same base is that you subtract the denomonator from the numerator. So let's simplify the first one, which is actually the most confusing.
Multiplying the exponents you get:
Subtracting the denominator from the numerator between the common base of p you get this:
Doing that math gives you
which equals 
which is 
, or the third one down.
The next one:
simplifies to:
and subtracting the power of the denominator from the power of the numerator gives you:
, which is the last choice.
simplifies to:
which simplifies very nicely to:
, which is the first choice. The other one is found by process of elimination!
Multiplying the exponents you get:
Subtracting the denominator from the numerator between the common base of p you get this:
Doing that math gives you
The next one:
simplifies to:
and subtracting the power of the denominator from the power of the numerator gives you:
simplifies to:
which simplifies very nicely to: