5.1,+5.2,+MR5+-+Olivia+C.+(7H)

=__Olivia V.F. Chaudhury__= =__Math 7H, Mr Cooper__= =__10 . 6 . 2010__=

=WHAT'S THE BIG IDEA?=

Observation and description of changes in the world around us are the first steps in finding and learning about patterns.
=...AND THE ESSENTIAL QUESTION?=

How can I visually explain situations where one thing depends on another?
= __ **Problem 5.1 ~ Graphing on a Calculator** __ =

= = = A1. The graphs that are similar are // y=3x-4 // and // y=3x+2 //. = = A2. They are similar because they both have straight, parallel lines that point in the same direction. = = A3. The equations for the graphs are similar because they have // x //as an independent variable with a fixed // 3 //. = = = = B1: // y=x² // has a different graph from the other equations. = = B2: This graph is a curved line but, however, the others are straight. = = B3: // x² //is the independent variable in this equation, while the other two have simply // x // as theirs. = = = = =

Set #2 Graph ~


= A1. // y=3x // and // y=1x //have similar graphs. = = A2. The lines are straight lines crossed at the 0,0 point. = = A3. The equations are similar because they contain// x // as the independent variable. = = = = B1: // y=5 // is the equation that has a different graph from the others. = = B2: This graph is a straight line, but it is not dependent on any other variables. = = B3: This equation does not contain// x //as an independent variable, while the other two equations have it. =

Set #3 Graph ~


= = = = = ** A1. // y=2x+3 //and // y=2x-5 // have similar graphs. ** = = ** A2. They are straight, parallel lines that point in the same direction. ** = = ** A3. The equations are similar because they contain// x // as their independent variable with 2 as a fixed number. ** = = = = ** B1: // y=0.5x+2 // has a different graph from the other two equations. ** = = ** B2: This graph is a straight line, but it is not parallel with the other two lines. ** = = ** B3: This equation contains // x // as the independent variable // 0.5 // as an fixed number, while the other two equations have // x // as the independent variable with 2 as an fixed number. ** = = =

=** __5.1 ~ Follow Up__ **=

1A. If // x //= // 2 //, what is // y //? Answer : // y //= // 4 //


 * 1B. If // x // = // 2/3 //, what is // y //? **
 * Answer : // y //= // 4/3 // **


 * 1C. If // x //= // 3.25 //, what is // y //? **
 * Answer : // y //= // 6.5 // **


 * 1D. Complete the table for the equation // y=2x // **** . **
 * Answer : **


 * ** x ** || ** 0 ** || ** 1 ** || ** 2 ** || ** 3 ** || ** 4 ** || ** 5 ** || ** 6 ** ||
 * ** y ** || ** 0 ** || ** 2 ** || ** 4 ** || ** 6 ** || ** 8 ** || ** 10 ** || ** 12 ** ||

** 2. Complete the table for the equation // y=2x+3 //. ** ** Answer : **
 * ** x ** || ** 0 ** || ** 1 ** || ** 2 ** || ** 3 ** || ** 4 ** || ** 5 ** || ** 6 ** ||
 * ** y ** || ** 3 ** || ** 5 ** || ** 7 ** || ** 9 ** || ** 11 ** || ** 13 ** || ** 15 ** ||

Answer : Both of the tables have the variables x and y, and have the same number of rows and columns. Also, the value of x remained the same in both tables, while y increased by 2’s.
=__Mathematical Reflections ~ 5__=

1A. Dear Friend,
==**In the past few days, I learned how to use a graphing calculator. I learned how to graph equations and I also learned which equations go through which axis. Another thing that I learned is that I do not have to clear my calculator screen to make the equations invisible.**==

2A. The rule for the number of tents per customer is //n/2t//. Here, the 'n' means the number of customers, and the 't' indicates the number of tents.
==2B. My graph gives enough information to make a graph or table. To make a table, I would replace 'n' with the correct number of customers and then calculating the number of tents. For a graph, I would plot the coordinate pairs.==

=__ **Summary**  __= == **This investigation taught me how to use a graphing calculator. i.e. graphing equations, turning equations into tables, etc. I also learned how to graph equations without the help of graphing calculators.** ==

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