Question

Which statement is always true?

A. A linear relationship is proportional.
B. A linear relationship is non-proportional.
C. A proportional relationship contains the point ( 0 , 0 ) .
D. A non-proportional relationship has a constant rate of change.

Answer 1

A

Explanation:

When we say proportional, we basically mean two quantities are based on a multiplicative constant. For example:

1:2 is proportional to 5:10, because if we reduce 5:10, we get 1:2.

Also, in terms of coordinate geometry, we can say line

y = ax

and

y = bx

are proportional if a:b = constant always.

We say that is a linear line. Linear relationship.

Now, looking at the answer choices, we can eliminate B and C [Choice C is easily eliminated because point (x,y) doesn't matter]. Also, we ccan eliminate D because this is just the opposite.

So answer choice A holds true.

A is right.

Answer 2

Option A. A linear relationship is proportional.

Explanation:

A linear relationship expresses the proportionality of the variable with respect to an output.

Let's take an example:

let the function be given as y

Let the proportionally constant be given as = C

Let the variable be = k

If we say, y is proportional to K, it means that:

y
`\alpha K`

but we need to introduce a constant and generate a linear proportionality

Therefore, the relationship becomes:

`y = CK`

The relationship will be proportional an is linear.