Question

Complete the following sentences.

In a relationship that varies directly, as one amount increases, the other amount blank In a relationship that varies inversely, as one amount increases, the other amount blank ASAP

Answer 1

1) Increases

2) Decreases

Explanation:

For direct proportion, the general equation is y= kx, where k is a constant.

Take for example the equation y= 4x.

When x= 1, y= 4(1)= 4

Since y is dependent on th value of x, let's substitute x with a larger number and see what happens to y.

When x= 3, y= 4(3)= 12

Notice that when x changes from 1 to 3, y increases from 4 to 12.

∴ In a relationship that varies directly, as one amount increases, the other amount increases.

Inverse proportion has a general equation of
`y = (k)/(x)`.

Let's use
`y = (4)/(x)` as an example.

When x= 1, y= 4÷1= 4

When x= 4, y= 4÷4= 1

This time, when x increases from 1 to 4, y decreases from 4 to 1.

∴ In a relationship that varies indirectly, as one amount increases, the other amount decreases.