Question

The Mathalot Company makes and sells textbooks. They have one linear function that represents the cost of producing textbooks and another linear function that models how much income they get from those textbooks. Describe the key features that would determine if these linear functions ever intersected.

Answer 1

The lines would intersect where the cost to produce is equal to the income they make. Hopefully the income line has a greater slope that would cause the money they make to overcome the amount they spend on producing the books.

Answer 2

Here are a number of rules relating to straight lines:

1) Parallel lines never intersect, unless they are one and the same line.
2) Two straight lines with different slopes will intersect.
3) Lines that coincide (see (1), above) have infinitely many solutions.

Which of these, rules seems to apply here?