Question

This graph shows a proportional relationship.

What is the constant of proportionality?


What is the answer as a ratio in simplified form in the box.

Answer 1

the constant proportionality is 2

Answer 2

k=
`(5)/(4)`

5:4 or 1:0.8

Explanation:

Since the graph ascends, it means when y(on the horizontal axis) increases, x (in the vertical axis increases)

This is an example of a direct proportion.

y=kx where k is the constant of proportionality.

From the point (
`((2)/(5) ,(1)/(2) )` given,

Using the (x,y) coordinate notation,
`x=(2)/(5) ,y=(1)/(2)`

Substituting into y=kx

`(1)/(2) =(2k)/(5)`

Next we solve for k by multiplying both sides by
`(5)/(2)`

`(1)/(2)X (5)/(2) =(2k)/(5) X (5)/(2)\\k= (5)/(4)`

Our answer as ratio in simplified form is given as 5:4 or 1:0.8