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, $|m_1|$, it means the absolute rate of change of second function is greater than the first function.

Therefore, the second function is changing more quickly.