The document contains a set of mathematical problems from a pre-test quiz for a Business Mathematics course. Here is a breakdown of the problems from the document:

1. Determine the demand function that passes through the points (3, 3) and (2, 4):

   • Options:
     • A. $P = x + 6$
     • B. $P = -x + 6$
     • C. $P = 2x + 6$
     • D. $P = -2x + 6$
     • E. $P = x - 6$

2. Find the intersection point of the lines $Y = 2 + 2x$ and $Y = 10 - 2x$:

   • Options:
     • A. (4, 6)
     • B. (2, 6)
     • C. (2, 5)
     • D. (3, 5)
     • E. (6, 2)

3. Given points A(2, 8) and B(4, 5), find the slope of line AB:

   • Options:
     • A. 15
     • B. 05
     • C. -15
     • D. -12
     • E. -05

4. Find the equation of the line passing through point (4, 1) with a slope of 2:

   • Options:
     • A. $Y = 7 - 2x$
     • B. $Y = 9 - 2x$
     • C. $Y = 2x - 7$
     • D. $Y = 2x - 9$
     • E. $Y = x + 4$

5. Calculate the value of $a$ so that the line $Y = ax + 2$ is parallel to the line passing through points (2, 4) and (3, 1):

   • Options:
     • A. $-3$
     • B. $3$
     • C. $2$
     • D. $4$
     • E. $-2$

Let me know if you'd like to see the solutions to any of these problems in detail or if you have any specific questions about the concepts.

Here are five relative questions you can explore:

1. How do you calculate the slope of a line given two points?
2. What is the formula for the equation of a line given a point and a slope?
3. How do you find the intersection of two linear equations?
4. What does it mean for two lines to be parallel in terms of their slopes?
5. How can you determine a demand function given two points?

Tip: When two lines are parallel, their slopes are equal! This is crucial in solving the fifth question.