Question

What is the constant of proportionality?

> A(8)
> B(14)
> C(16)
> D(48)

Answer 1

Can you read one point off the graph?

Answer 2

Other than (0, 0).

Answer 3

For example, when the x-coordinate is 2, what is the y-coordinate?

Answer 4

(2,16)

Answer 5

Correct.
That is a good point you read off the graph.

A direct relation has this form:

\(y = kx\)

where k is called the "constant of proportionality."

Answer 6

You have read one point off the graph, (2, 16).
Since we are dealing with a direct relation, it has to work in the form above.
We have an x-coordinate and a y-coordinate, so we replace x and y with them:

y = kx

16 = k * 2

Now solve for k.
What do you get for k?

Answer 7

8

Answer 8

Great.
Now that we know that k = 8, instead of just writing the general form of a direct relation, we can write the specific direct relation we have in this problem by replacing k with 8.

\(y = 8x\)

Notice that this relation we now have works with all the other points you can read off the graph.
(3, 24), (4, 32), (5, 40)

That means y = 8x is definitely the correct direct relation for our graph.

The constant of proportionality is k in y = kx, so in our case, since we have y = 8x, the constant of proportionality is 8.

Answer 9

ok THANKS SO MUCH now i understand

Answer 10

You're welcome.