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

Answer:

$y=5x$

Step-by-step 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

$y=5x$