Question

Which one of these relationships is different than the other three? Explain how you know. Hint: Find all

of the constants of proportionality.

Answer 1

Graph 2 has a different constant of proportionality

Explanation:

See attachment for graphs

To calculate the constant of proportionality, we simply determine the slope of each graph using

`m = (y_2 - y_1)/(x_2 - x_1)`

Where x's and y's are corresponding values of x and y

Graph 1:

`(x_1,y_1) = (0,0)`

`(x_2,y_2) = (0.8,4)`

Substitute these values in:
`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (4 - 0)/(0.8 - 0)`

`m = (4)/(0.8)`

`m = 5`

Graph 2:

`(x_1,y_1) = (0,0)`

`(x_2,y_2) = (10,55)`

Substitute these values in:
`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (55 - 0)/(10 - 0)`

`m = (55)/(10)`

`m = 5.5`

Graph 3:

`(x_1,y_1) = (0,0)`

`(x_2,y_2) = (4,20)`

Substitute these values in:
`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (20 - 0)/(4 - 0)`

`m = (20)/(4)`

`m = 5`

Graph 4:

`(x_1,y_1) = (0,0)`

`(x_2,y_2) = (10,50)`

Substitute these values in:
`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (50 - 0)/(10 - 0)`

`m = (50)/(10)`

`m = 5`

From the calculations above, graph 2 has a different constant of proportionality of 5.5 while others have 5 as their constant of proportionality