Question

When a bill is not paid by the due date, a late fee is added each month until the bill is paid. The values in the table represent the total amount due, in dollars, for each month that a payment remains overdue.
Months | Total due
2 300
5 375
10 500
Using x for the number of months overdue and y for the total amount due, in dollars, construct a linear function that describes the relationship between the number of months the bill is overdue and the total amount due. Enter the equation of the function in the box

Answer 1

The total amount due, in dollars, is an illustration of a linear function

The equation of the function is $y = 25x + 250$

Represent the month with x, and the total due with y.

Start by calculating the slope (m) using:

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

So, we have:

$m = \frac{375 - 300}{5 - 2}$

Simplify

$m = \frac{75}{3}$

Divide 75 by 3

$m = 25$

The linear equation is then calculated as:

$y = m(x - x_1) + y_1$

So, we have:

$y = 25(x - 2) + 300$

Open bracket

$y = 25x - 50 + 300$

Add 300 to -50

$y = 25x + 250$

Hence, the equation of the function is $y = 25x + 250$

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