Question

the question i have says “which statement correctly compares the rates of change of the two functions” and i dont understand how to solve it

Answer 1

The rate of change of function A is 4

The rate of change of function B is 3 (option D)

Step-by-step explanation:

We are looking for the rate of change of two functions.

m is also known as the rate of change

`\begin{gathered} \text{Function A is given as:} \\ y\text{ = 4x + 6} \end{gathered}`

comparing the equation above to a linear function:

y = mx + b

m = slope , b = y -intercept

For function A:

m = slope = 4, b = 6

To get the rate of change of function B, we need to find the slope of any two points on the table.

For linear function, the slope is constant irrespective of the two points used in calculating it.

Formula for slope:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

using points; (1, 3) and (3, 9)

`\begin{gathered} x_1=1,y_1=3,x_2=3,y_2\text{ = 9} \\ \text{slope = }(9-3)/(3-1) \\ \text{slope = }(6)/(2) \\ \text{slope = 3} \\ \text{Slope for function B is 3} \end{gathered}`

The rate of change of function A is 4

The rate of change of function B is 3 (option D)