Question

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Answer 1

Table c

Explanation:

Required:

Which of the 4 has the greatest rate of change

For Graph (A):

We start by picking any two equivalent points on the table:

`(x_1,y_1) = (0,1)`

`(x_2,y_2) = (2,5)`

Next, we determine the slope, m:

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (5-1)/(2-0)`

`m = (4)/(2)`

`m = 2`

This represents the rate of change:

For (B):
`y = 3x + 7`

An equation is of the form:

`y = mx + b`

Where

m represents slope or rate of change:

By comparison:

`m = 3`

For table (C):

We start by picking any two equivalent points on the table:

`(x_1,y_1) = (1,7)`

`(x_2,y_2) = (2,12)`

Next, we determine the slope, m:

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (12-7)/(2-1)`

`m = (5)/(1)`

`m = 5`

This represents the rate of change:

For (D):

The $1.00 paid every week represents the rate of change.

So:

`m = 1`

For A - D:

The rate of change are:

`A = 2`

`B = 3`

`C = 5`

`D = 1`

5 is the greatest.

Hence, (c) has the greatest rate of change