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Let's analyze the question step by step.

### Part (a): Finding the Equation of the Line for Cost of Manufacture
The cost of manufacturing the toy cars involves two parts:
- **Fixed cost**: \$200 per day (constant).
- **Variable cost**: The cost of producing each toy car.

The graph shows a straight line, which means it's a linear equation. The general form of a linear equation is:
\[
C = mN + b
\]
Where:
- $C$ is the total cost,
- $N$ is the number of toys,
- $m$ is the slope (which represents the cost per toy),
- $b$ is the y-intercept (which represents the fixed cost).

From the graph:
- The **y-intercept** is 200, which corresponds to the fixed cost. So, $b = 200$.
- The slope $m$ can be calculated by observing the rise over run. Between 5 toys (\$400) and 15 toys (\$1000), the cost increases by:
  \[
  m = \frac{1000 - 400}{15 - 5} = \frac{600}{10} = 60
  \]

Thus, the equation for the cost of manufacture is:
\[
C = 60N + 200
\]

### Part (b): Drawing the Line for Income from Sales
The business sells each toy car for \$80, so the income line is also linear, and its slope represents the income per toy.

The equation for income $I$ is:
\[
I = 80N
\]
Here, there is no fixed component (like the cost), so the y-intercept is 0. The slope is 80, meaning for each toy sold, the income increases by \$80.

To draw this line on the graph, it should pass through:
- The origin (0, 0),
- The point where 10 toys generate \$800 in income (10, 800),
- The point where 20 toys generate \$1600 in income (20, 1600).

Would you like any more details on this solution, or any additional explanation?

### Follow-Up Questions:
1. How would the graph change if the fixed cost was higher, say \$300?
2. What would happen if the sale price per toy decreased to \$70?
3. How can we find the break-even point where the cost equals the income?
4. How would a higher variable cost per toy affect the slope of the cost line?
5. What equation would represent the profit made from selling the toys?

### Tip:
Always identify the slope and intercept when dealing with linear equations, as they provide direct information about rate of change and starting values.

A small business manufactures toy cars, which it sells for $80 each. The graph below shows the line which represents the cost of manufacturing the toy cars in each day’s production run. There are fixed costs each day which amount to $200, and a cost associated with producing each toy car.
(a) What equation would describe the line shown?
(b) On the graph above, draw the line which would represent the income from sales of the toy cars.

Explore how to determine the cost equation for manufacturing toy cars and calculate income from sales using linear equations. Learn the concepts of slope, intercept, and how they apply to real-world business problems. Suitable for students in Grades 9-11.

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