2.3+Testing+Whether+Driving+Fast+Pays+0910

Cherub Sharma 28th August, 2009 Block F Advanced Math Grade 8

** 1.1 **  ** BIG IDEA ** : Many real world situations can be modelled and predicted using mathematics.


 * Essential question: ** How can I model a non-linear relationship?


 * 1) Copy and complete the table below to show the time it would take for the 300-mile trip at various average speeds.


 * Average speed (miles per hour) || Trip time (hours) ||
 * 30 || 10 ||
 * 40 || 7.5 ||
 * 50 || 6 ||
 * 60 || 5 ||
 * 70 || 4.29 ||


 * 1) Make a graph of the relationship between the average speed, //S,// and the time, //T.//

The equation for the relationship can be found using the following steps:
 * 1) Find an equation for the relationship between //S// and //T.//

· Take any two coordinates from your line on the graph. · Use the formula **__Y2-Y1 / X2-X1__** to find the slope · Substitute the values of X and Y from a coordinate on the line to the equation Y=MX+B · Write down the equation for the line

Thus the equation for this line is y = -1/6x+15

I think that this is a non linear relationship because I could not find any sort of pattern or sequence in the x’s and y’s. In the graph we can clearly see that the line is not straight. Thus we can infer that it is not a linear equation.
 * 1) Is this relationship between S and T linear of or non-linear? Explain how the table, the graph, and the equation support your answer.

** FOLLOW UP ** a) Yes, I agree with the bus driver because increasing the speed would decrease the time and increase the distance; thus covering a longer distance in a shorter time.  b)  The answer is illustrated in the graph in a curve. The ‘x’ axis shows the average speed whereas the ‘y’ axis shows the time taken. The graph would quite be in the same position except that it would go a bit higher than the 300 mile. The values in the table would be different as the number of hours taken for the trip would increase. The equation would change accordingly as well.
 * 1) The bus driver figured out that if he increased his average speed from 40 to 45 miles per hour, the time for the trip would be shortened from 7.5 hours to 6.67 hours, a saving of 50 minutes. He then reasoned that increasing his average speed from 45 miles to 50 miles per hour would cut another 50 minutes off the trip, and increasing his average speed from 50 to 55 miles per hour would cut another 50 minutes off the trip.
 * 1) How would the table, the graph, and the equation change if the trip were 500 miles instead of 300 miles?

The equation for the problem 2.2 is **y=1/10x+1**
 * 1) Look back at your from Problem 2.2. Find an equation for the relationship you explored in that problem?