Question

The price for footballs. Derive the equation of the proportional relationship through the origin
first point (1,9) second point (2, 18) third point (3, 27) fourth point (4, 36)

Answer 1

To derive the equation of the proportional relationship through the origin from the given points, we need to identify the constant of proportionality.

The points you provided are:
- (1, 9)
- (2, 18)
- (3, 27)
- (4, 36)

In a proportional relationship, if \( y \) is directly proportional to \( x \), then the relationship can be expressed as:

\[
y = kx
\]

where \( k \) is the constant of proportionality.

We can find \( k \) using any of the points provided. Let's use the first point (1, 9):

Given \( x = 1 \) and \( y = 9 \):

\[
9 = k(1)
\]
\[
k = 9
\]

Now, we can write the equation of the proportional relationship:

\[
y = 9x
\]

To confirm this relationship holds for the other points:

- For (2, 18):
\[
y = 9(2) = 18 \quad \text{(correct)}
\]

- For (3, 27):
\[
y = 9(3) = 27 \quad \text{(correct)}
\]

- For (4, 36):
\[
y = 9(4) = 36 \quad \text{(correct)}
\]

Thus, the derived equation of the proportional relationship through the origin is:

\[
y = 9x
\]