Question

A. Their rates of change differ by 2. B. Their rates of change differ by 4. C. Function M has a greater rate of change than Function P. D. Function M and Function P have the same rate of change.

Answer 1

Answer:

(a) Their rates of change differ by 2

Step-by-step explanation:

Given

See attachment for functions M and P

Required

Determine what is true about the rates of M and P

First, we calculate the slope (i.e. rate) of both functions.

Slope is calculated as:

$m = \frac{y_2 -y_1}{x_2 - x_1}$

From the table of M, we have:

$(x_1,y_1) = (-2,-9)$

$(x_2,y_2) = (2,11)$

So, the slope is:

$m_M = \frac{11 --9}{2--2}$

$m_M = \frac{20}{4}$

$m_M = 5$

For function P, we have:

$y = 7x + 9$

A function is represented as:

$y = mx + b$

Where:

$m = slope$

So, by comparison:

$m_P = 7$

At this point, we have:

$m_M = 5$ --- Slope of M

$m_P = 7$ --- Slope of P

Only option (a) is true because both slopes differ by 2. i.e. 7 - 5 = 2

Other options are not true