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:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
From the table of M, we have:
[tex](x_1,y_1) = (-2,-9)[/tex]
[tex](x_2,y_2) = (2,11)[/tex]
So, the slope is:
[tex]m_M = \frac{11 --9}{2--2}[/tex]
[tex]m_M = \frac{20}{4}[/tex]
[tex]m_M = 5[/tex]
For function P, we have:
[tex]y = 7x + 9[/tex]
A function is represented as:
[tex]y = mx + b[/tex]
Where:
[tex]m = slope[/tex]
So, by comparison:
[tex]m_P = 7[/tex]
At this point, we have:
[tex]m_M = 5[/tex] --- Slope of M
[tex]m_P = 7[/tex] --- Slope of P
Only option (a) is true because both slopes differ by 2. i.e. 7 - 5 = 2
Other options are not true
