Question

Compare the rate of change of the given functions and choose the correct option.

Function A: y = 5.5x + 8

Function B: It is a linear function passing through the points (0,30) and (6,0)

Function C:

• A. $\text{Function A}>\text{Function C}>\text{Function B}$
• B. $\text{Function B}>\text{Function C}>\text{Function A}$
• C. $\text{Function C}>\text{Function A}>\text{Function B}$
• D. $\text{Function B}>\text{Function A}>\text{Function C}$

Answer 1

The correct option is A $\text{Function A}>\text{Function C}>\text{Function B}$

Given,
Function A: y = 5.5x + 8

The above equation is in the form of:
y = mx + c

where 'm' indicates the slope which also known rate of change.

Comparing the equation y = 5.5x + 8 with y = mx + c

Slope = rate of change of A = 5.5

Function B:

Given, it is a linear function and passes through (0,30) and (6,0).

$\therefore \text{Rate of change}=\frac{\text{Change in y}}{\text{Change in x}}$

$=\frac{0-30}{6-0}$

$=-5$

Function C:
From the graph the line passes through the coordinates (0,4) and (4,20).

$\therefore \text{The rate of change}=\frac{\text{Change in y}}{\text{Change in x}}$

$=\frac{20-4}{4-0}$

$=4$

Hence, the order of rate of change is
$\text{Function A}>\text{Function C}>\text{Function B}$