. A printer costs a price of Birr 1,400 for printing 100 copies of a report and Birr 3000 for printing 500

We can interpret this as a linear relationship between the cost and the number of copies printed. Let's determine the cost per copy by setting up a linear equation:

Let:
- \( C \) represent the total cost in Birr.
- \( x \) represent the number of copies printed.

We have two points to form a linear equation in the form \( C = mx + b \):
1. When \( x = 100 \), \( C = 1400 \).
2. When \( x = 500 \), \( C = 3000 \).

### Step 1: Determine the slope \( m \)
The slope \( m \) is calculated as:
\[
m = \frac{C_2 - C_1}{x_2 - x_1} = \frac{3000 - 1400}{500 - 100} = \frac{1600}{400} = 4
\]

So, the cost per additional copy is 4 Birr.

### Step 2: Determine the y-intercept \( b \)
Using the equation \( C = mx + b \), we can plug in one of our points, say \( (100, 1400) \):
\[
1400 = 4(100) + b
\]
\[
1400 = 400 + b
\]
\[
b = 1000
\]

### Step 3: Write the equation
Now we have the linear equation that models the cost:
\[
C = 4x + 1000
\]

### Explanation
This equation \( C = 4x + 1000 \) implies:
- A fixed cost of 1000 Birr, regardless of the number of copies printed.
- An additional cost of 4 Birr per copy.

Would you like further details or have any questions?

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Here are some related questions:
1. What would be the cost for printing 200 copies?
2. If the budget is limited to 5000 Birr, how many copies can be printed?
3. What is the marginal cost of printing an additional copy?
4. Can this linear model apply to all quantities of printing, or is it limited to specific ranges?
5. What are other factors that could influence printing costs in real-life scenarios?

**Tip:** When analyzing linear costs, break down the problem into fixed and variable components for clarity.

A printer costs a price of Birr 1,400 for printing 100 copies of a report and Birr 3000 for printing 500.

Calculate the linear equation modeling printing costs, given prices for printing 100 and 500 copies. This analysis covers slope determination, fixed and variable costs, and how to interpret the equation C = 4x + 1000. Ideal for Grades 8-10 math students exploring linear relationships in real-world contexts.

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