Question

let y represent the total cost of publishing a book (in dollars). let x represent the number of copies of the book printed. suppose that x and y are related by the equation y = 1150 + 15x.
answer the questions below.
note that a change can be an increase or a decrease.
for an increase, use a positive number. for a decrease, use a negative number.
(a) what is the change in the total cost for each book printed?
$
(b) what is the cost to get started (before any books are printed)?
$

Explanation:

Part (a)

Step 1: Identify the slope

The equation is in the form \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept. For the equation \( y=1150 + 15x \), the slope \( m = 15 \).
The slope represents the change in \( y \) (total cost) for a unit change in \( x \) (number of books printed). So the change in total cost for each book printed is \( 15 \) dollars.

Part (b)

Step 1: Find the cost when \( x = 0 \)

When no books are printed (\( x = 0 \)), we substitute \( x = 0 \) into the equation \( y=1150+15x \).
\( y=1150 + 15\times0=1150 \). This value of \( y \) when \( x = 0 \) represents the fixed cost or the cost to get started.

Answer:

(a) The change in total cost for each book printed is \(\$15\).
(b) The cost to get started (before any books are printed) is \(\$1150\).