Question

Three functions are defined as:

Function A: y = 2.5x + 10

Function B: It has a x-intercept of 25 and y-intercept of 10.

Function C:


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

• A. Slope of B > Slope of C > Slope of A
• B. Slope of B > Slope of A> Slope of C
• C. Slope of C = Slope of A > Slope of B
• D. Slope of C > Slope of A > Slope of B

Answer 1

The correct option is D Slope of C > Slope of A > Slope of B

We have to find the rate of change of a function for different situations.

Equation of Function A is y = 2.5x + 10

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

We know in the equation y = mx + c, "m" indicates the slope which is also known rate of change of a function.

∴ Slope = rate of change of = 2.5
Function A

For Function B:


The graph cuts the y-axis at (0,10) and the x-axis at (25,0).

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

$=\frac{0-10}{25-0}$

$=-0.4$

So, rate of change of B = 0.4

For Function C, we observe:


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

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

$=4$

So, the rate of change of C = 4

From the above values, we get:
$\text{Slope of C}>\text{Slope of A}>\text{Slope of B}$