Question

The table below shows the values of y for different values of x:

x y
0
0
1
5
2
10
3
15


Which equation shows the relationship between x and y?

Answer 1

`y=5x`

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`y/x=k` or
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

we have

For x=0, y=0 -----> the line passes through the origin

For x=1, y=5 ---->
`k=y/x=5/1=5`

For x=2, y=10 ---->
`k=y/x=10/2=5`

For x=3, y=15 ---->
`k=y/x=15/3=5`

so

The constant of proportionality is k=5

The table represent a direct variation

The equation is equal to
`y=kx`

substitute the value of k

`y=5x`