2.5+Crossing+the+Line

AM Big idea**: Many real world situations can be modeled and predicted using mathematics
 * 31/05/09
 * Essenital questions:** What is the relationship between a table, a graph and an equation?


 * __Problem 2.5 and Follow Up__**


 * A1. Make a table showing the distance each brother is from the starting line at several different times during the first 40 seconds.**
 * Time (seconds) || Emile || Henri ||
 * 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 each brother is from the starting line for both brothers.

3. Write an equation for each brother showing the relationship between he time and distance from the starting line.** Emile: y= 5x+45 Henri: y=12.5x


 * 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.**
 * Emile will overtake Henri 76 meters (or more) from the starting line. You can use the table to answer this question by finding the point when they are both at the same distance. You can use the graph to answer this by finding when the line that represents Emile's distance crosses over the line that represents Henri's.

Emile will overtake Henri after 30 seconds. You can use the table to answer this by finding the point when they are at the same distance (and go a little further). You can use a graph to answer this question to
 * C. After how many seconds will Emile overtake Henri? Explain how you can use the table and the graph to answer this question.**

__**Follow Up**__ After three seconds Henri will be ahead by 40.5 meters.
 * 1.****After three seconds who will be ahead? By how much?** ||

Henri will be 49 meters away from the line.
 * 2. How far will Henri be from the starting line when Emile has walked 10 meters?**

The graph with Emile’s data is steeper because the coefficient for x in his case is larger.
 * 3a. which graph is steeper?**

You can determine which line is steeper from a table by finding the line with a greater y value for every x value. You can determine which line is going to be steeper from an equation by finding the equation with the greater coefficient for x. 4. Explain how you can use graphs, tables and equations to determine how far each brother will be from the starting point after 5 minutes. You can use a graph to determine how fast do the brothers will be, by finding how far he is at one second and then multiplying that by 60 because there are 60 seconds in a minute, after you get your answer you can multiply that by 5 which would give you the distance for 5 minute. Ex: for Emile it would be; (1, 2.5) 2.5m/s 2.5x60= 150m/min 150x5=750m in five minutes You could use a table by either making a table in intervals of 5 and make the time go up to 60sec or you could just do what you did with the graph. You could use an equation by just finding how many seconds there is in 5mins which is 60x5=300 and multiply your y value by 300 and you’ll get the distance. Ex: Henri’s equation: y= 1x+45 1x300+45=345
 * b. How can you determine which of two lines will be steeper from their tables? From their equations?**

Emile’s graph crosses the y-axis at (0, 0) and Henri’s graph crosses the y-axis at (0, 45). In terms of the race this means that from then on everything is positive. You can predict when a graph will cross the y-axis from a table when x is 0 and you can predict when a graph will cross the y-axis from an equation when you substitute x for 0.
 * 5a. at what points do Emile and Henri’s graphs cross the y axis? What does this 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?**


 * 6a. Emile’s friend Yvette joins the race and has a head start of 20m and walks at 2m/s. Copy and complete the table below to show Yvette’s distance from the starting line for 0-7 seconds.**

Time (seconds) || Distance (meters) || 0 || 20 || 1 || 22 || 2 || 24 || 3 || 26 || 4 || 28 || 5 || 30 || 6 || 32 || 7 || 34 ||
 * b. Which of the following gives the 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**

I think that the answer is v, none of the above although i could work but it isn't in the right order.