Introduction to 3.3

  1. You need to rent a mountain bike Saturday. You know two companies that rent bikes. Best Bikes charges $2.50 per hour plus a $5non-refundable deposit. Nice Bikes charges $2 per hour plus a $10 non-refundable deposit.

a)Create 2 equations (one for each bike shop) to describe the relationship between cost and time.

b)Complete the following tables for the two companies.

Best BikesNice Bikes

x – hours y – total costx – hours y – total cost

0 0

1 1

2 2

3 3

4 4

c) Graph the data in the tables. Place both on the same Cartesianplane.

Set up the axes as follows: x axis0 to 15 in units of 1

y axis0 to 40 in units of 2

d)If the lines are extended they will intersect. What is true about the coordinates where the lines intersect? Extend your lines to find the intersection point. Explain what the intersection point represents.

e)Which bike shop should you use if you need a bike for 15 hrs? How did you decide?

  1. During a storm day last year it snowed 3 cm per hour. During another storm day it snowed 2 cm per hour but there were already 12 cm on the ground before it started.

a)Create 2 equations (one for each day) to describe the relationship between the amount of snow and time.

b) Complete tablesfor each day to show the amount of snow for 0-4 hrs.

c) Graph the data in the tables. Place both on the same Cartesian plane.

Set up the axes as follows: x axis 0 to 15 in units of 1

y axis 0 to 40 in units of 2

d)Find the point of intersection by extending the lines. Explain what the intersection point represents.

e)On which Day was there more snow at 10 hrs?

  1. During a day last year Bob was filling his pool while Jack was draining his. Bob started with an empty pool and put in 100 liters per hour. Jack had 2 000 liters in his pool and drained 100 liters per hour.

a)Create 2 equations (one for Bob and one for Jack) to describe the relationship between the amount of water and time.

b)Complete tables for each person to show how much water was in each person’s pool for 0-5 hrs.

c) Graph the data in the tables. Place both on the same Cartesian plane.

Set up the axes as follows: x axis 0 to 15 in units of 1

y axis 0 to 2000 in units of 100

d) Find the intersection point by extending the lines. Explain what the intersection point represents.

  1. a) Can you think of ways other than graphing to find the intersection points you found above? Hint: Thinking about what the intersection point you are finding represents should help. Try finding the intersection points again using your ideas.

b) Briefly summarize your new ideas to find intersection points.

Finding Intersection Points

For # 1-3 determine the intersection point by doing either (a) or (b).

  1. There are two ice rinks in your town. The Palace charges $75 per hour. The Barn charges $50 up front and $70 per hour.

a) Complete a table of values for each rink to show the cost for 0-4 hrs.

Graph the data in the tables. Set up the axes as follows: x axis 0 to 15 in units of 1.

y axis 0 to 1 000 in units of 50.

Extend the lines to find the intersection point. Explain what the intersection point represents.

b) Sketch a graph for the rinks. What does the intersection point represent?

Create two equations (one for each rink) to describe how much each rink charges. Use your equations to find the intersection point.

  1. You and your friend decided to have a race in the stairwell in your building. You started at the bottom and ran up 2 floors per minute. Your friend started on the 48th floor and ran down 4 floors per minute. Interpret your solution.

a) Complete a table of values for each person to show the floor each was on for 0-4 minutes.

Graph the data in the tables. Set up the axes as follows:x axis 0 to 12 in units of 1.

y axis 0 to 48 in units of 4.

Extend lines to find the intersection point. Explain what the intersection point represents.

b)Sketch a graph for the 2 people. What does the intersection point represent? Create two equations (one for each person) to describe the floor each boy was on in relation to the minutes ran. Use your equations to find the intersection point. Interpret your solution.

  1. During the Christmas holiday John put two candy canes on the tree each day. Mary had 60 candy canes on her tree and ate 3 per day.

a) Complete a table of values for each person to show the # of canes cost for 0-4 days.

Graph the data in the tables. Set up the axes as follows:x axis 0 to 16 in units of 1.

y axis 0 to 60 in units of 3.

Extend the lines to find the intersection point. Explain what the intersection point represents.

b)Sketch a graph for the 2 people. What does the intersection point represent? Create two equations (one for each person) to describe how many canes were on the tree in relation to the days. Use your equations to find the intersection point. Interpret your solution.

  1. For each question, determine the point of intersection by using algebra or graphing.

a) y = -2x + 4 y = 2x – 20 if graphing x axis -2 to 10 in units of 1.

y axis - 24 to 4 in units of 1

b) y = 2x + 10 y = -3x – 5 if graphing x axis -6 to 4 in units of 1.

y axis -14 to 16 in units of 2.

c) y = 2x y = - 2x + 4 if graphing x axis -2 to 2 in units of 1.

y axis -4 to 8 in units of 1.