2.5++Crossing+the+Line+10-11

Marta Fiorillo
Math 7B May 15th, 2011

=2.5 Crossing the Line=

**Big Idea**: Many real world situations can be modeled and predicted using mathematics.
=**Essential Questions:** What is the relationship between a table, a graph and an equation?=

(sec) || Emile || Henri ||
 * A. 1) Make a table showing the distance each brother is from the starting line at several different times during the first 40 seconds.**
 * Time
 * 0 || 0 || 45 ||
 * 5 || 12.5 || 50 ||
 * 10 || 25 || 55 ||
 * 15 || 37.5 || 60 ||
 * 20 || 50 || 65 ||
 * 25 || 62.5 || 70 ||
 * 30 || 75 || 75 ||
 * 35 || 87.5 || 80 ||
 * 40 || 100 || 85 ||


 * 2) On the same set of axes, graph the time and the distance from the starting line for both brothers.**

__Emile:__ //y// = 5//x// + 45 __Henry__: //y// = 12.5//x//
 * 3) Write an equation for each brother showing the relationship between the time and the distance from the starting line.**

Emile will overtake Henri by 75 meters because on the graph that"s where the lines meet and on the table, it"s where they have the same number.
 * B. How far from the starting line will Emile overtake Henri? Explain how you can use the table and the graph to answer this question.**

Emily will overtake Henri in 30 seconds. You can tell because on the graph it"s where the two lines meet and on the table it"s where they have the same distance.
 * C. After how many seconds will Emile overtake Henri? Explain how you can use the table and the graph to answer this question.**

=Problem 2.5 Follow-Up=

I think Henri, because he got a head start. He would be ahead by about 40 meters.
 * 1. After 3 seconds, who will be ahead? By how much?**

I think Henri would have walked about 48 meters.
 * 2. How far will Henri be from the starting line when Emile has walked 10 meters?**

Emile"s is steeper because he makes more steady progress. I think you can tell by seeing who would make more progress if they kept a steady pace.
 * 3. a. Which graph is steeper?**
 * b. How can you determine which of two lines will be steeper from their tables? From their equations?**

__graph__- see how far he is at 10 seconds then multiply it by 6, then by 5. __table__- make it with intervals of 5, make it go up to 60 then multiply it by 5. __equation__- change the //x// to 60 then times what you get by 5.
 * 4. Explain how you can use the table, the graph, and the equations to determine how far from the starting line each brother will be after 5 minutes.**

__Emile__: (0,0) __Henry__: (0,45) This represents when they start. __graph__- extrapolate the graph. __equation__- put the //x// as 0 and the value of y will be calculated to know where the graph intersects the //y-//asix.
 * 5. a. At what points do Emile"s and Henry"s graphs cross the y-axis? What do these points mean in terms of the race?**
 * b. How can you predict where a graph will cross the y-axis from a table? From an equation?**


 * 6. Emile"s freidn Yvette joins the race. Yvette had a head start of 20 meters and walks at 2 meters per second.**
 * a. Copy and complete the table below to show Yvette"s distance from the starting line for 0 to 7 seconds.**

(sec) || Distance ||
 * Time
 * 0 || 20 ||
 * 1 || 22 ||
 * 2 || 24 ||
 * 3 || 26 ||
 * 4 || 28 ||
 * 5 || 30 ||
 * 6 || 32 ||
 * 7 || 34 ||

I think //y// = 20 + 2//x// is the best answer.
 * b. Which of the following equations gives the relationship between Yvette"s distance from the starting line, d, and the time, t?**
 * i.** //d = 20 + 2t//
 * ii.** //d = 2 + 20//
 * iii.** //d = 20t + 2//
 * iv.** //d = 20 + t//
 * v.** //none of the above//