Linear Relationship Open-ended Questions

I'm working on asking more conceptual, open-ended questions in order to challenge students, encourage critical thinking, utilize the "Rule of 4", and prepare students for AP Calculus level of rigor. The questions below represent my first serious attempt. Visit ilovemath.org for the full pdf.

---------- ---------- ---------- ---------- ---------- ---------- ---------- ---------- ----------

1. Give an example of a linear relationship in graphical, numeric, and analytic (equation) forms. Use the same linear relationship for all three representations.
2. What is the relationship between the slope formula and the point-slope form of a line? (How can you derive one from the other?)
3. How can you identify two perpendicular ! lines if they are both in General Form? (What is special about the numbers A, B, and/or C between the two equations)
4. Why is the “intercept form” given its name? (What makes it different from the slope-intercept form?). Also, give an example of a linear relationship in intercept form and graph the line.
5. Will 2 pair of parallel lines that are perpendicular to each other always form a square on their interior? If so, state how you know and if not, provide a counter example.
1. If : L1 || L2 and L3 || L4 , L1 _|_ L3 and L4 , L2 _|_ L3 and L4
2. Then: Does the interior of these lines always form a square?
6. Given the four lines described in question 5, if you multiplied the slopes of the 4 lines together, what would be the product?
7. Do the following four points form a parallelogram? How do you know if it does or does not. Points: (−4,0), (2,4), (−2,−3), (4,1)
8. The table below! gives the price, the supply, and the demand, for a certain vi! deo game .
   
1. Graph the points representing price & supply and the points representing price & demand.
2. Estimate the price at which the supply of video games will equal the demand. Also estimate the quantity that is supplied/demanded at this price.
3. What happens to the supply and to the demand when the price of the video game is higher than the price you found in part b? .... lower than the price of b?
   
   

Linear Functions and Slope Forms