Question

This graph shows a proportional relationship.

What is the constant of proportionality?

Enter your answer as a ratio in simplified form in the box.

Answer 1

The constant of proportionality is
`(9)/(8)`

Solution-

The constant of proportionality is the slope of the line, representing the relationship between the two variables.

The line passes through origin (0, 0) and
`((2)/(3),(3)/(4))`

We know that slope 'm' of the line joining (x₁, y₁) and (x₂, y₂) is,

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

Putting the values,

`m=((3)/(4)-0)/((2)/(3)-0)`

`=((3)/(4))/((2)/(3))`

`=(3* 3)/(2* 4)`

`=(9)/(8)`