Question

After 8 months, you have been able to save $937. You have the ability to save $130 per month. Build a model and write an explanation of the y- intercept. What is the rate of change?

Answer 1

Given:

After 8 months, you have been able to save $937.

You have the ability to save $130 per month.

To find:

The model for the situation and y-intercept and rate of change.

Solution:

Let y be the ability to saving after x months.

Ability to save in one month = $130

Ability to save in x months = $130x

So, total ability is

$y=130x+b$      ...(i)

where, b is initial savings.

After 8 months, you have been able to save $937.  So, the point is (8,937).

Put x=8 and y=937 in (i),

$937=130(8)+b$

$937=1040+b$

$937-1040=b$

$-103=b$

So, the y-intercept is -103. Here, negative sign represents that we cannot able to save initially or we have loan or liabilities of $103.

Put b=-103 in (i).

$y=130x+(-103)$  

$y=130x-103$

On comparing with slope intercept form, we get

Slope = 130 and y-intercept = -103

Therefore, the slope is 130 and y-intercept is -103.