Question

The equations of two functions are y=-21x+9 and y=24x+8 which function is changing more quickly? Explain

Answer 1

Given:

The equations are

`y=-21x+9`

`y=24x+8`

To find:

Which function is changing more quickly.

Solution:

The slope intercept form of a line is

`y=mx+b`

Where m is slope and b is y-intercept.

On comparing
`y=-21x+9` with the slope intercept form, we get

`m_1=-21`

`|m_1|=|-21|`

`|m_1|=21`

On comparing
`y=24x+8` with the slope intercept form, we get

`m_2=24`

`|m_2|=24`

Since,
`|m_1|<|m_2|`, it means the absolute rate of change of second function is greater than the first function.

Therefore, the second function is changing more quickly.