INTRODUCTION - fill the blank for full credit
bank: dependent, output, relationship, independent, variable, input
An equation (for example y = 2x, y could be the number of ears in a class and x the number of students)
describes a _______________ between variables, and a graph helps you "picture"this ____________.
A line graph pictures how change in one ___________ (x) go with changes in a second ___________ (y)
x is called the ____________ variable (the ________or manipulated variable) and y the ___________ variable
(the _________ or responding variable).

PART1: you need a meter stick + bouncing ball +tape
In this part, you will find out if there is a relationship between the height a ball is dropped and the height it bounces.

step1: tape a meter stick along the wall. Drop a ball as close as possible to meter stick. Start to drop the
ball from a height = 20cm. Measure the height dropped ___________. Repeat the experiment about 3 times.
 Every one in the team should do the experiment. . Fill the first line of the table 1 below.

step2: repeat step1 with a height dropped = 25cm, 30cm, 35cm .... 50cm/ Fill the table 1

DATA TABLE 1 : height bounced vs height dropped
x= height dropped (cm)	trial 1: height bounced (cm)	trial 2: height bounced (cm)	trial 3: height bounced (cm)	y= Average: sum (height bounced)/3
20	_____________	_____________	_____________	_____________
25	_____________	_____________	_____________	_____________
30	_____________	_____________	_____________	_____________
35	_____________	_____________	_____________	_____________
40	_____________	_____________	_____________	_____________
45	_____________	_____________	_____________	_____________
50	_____________	_____________	_____________	_____________

ANALYSIS.  As always, try without hint first.

1) Fill the last column of the TABLE. In Science, you usually find the average of a measured quantity
to try to get rid of some of the human errors.

2) The first column is your independent variable x or input. The last column is your dependent variable y
or output. Report the x values and the y values in the following table:

x = input height dropped cm	y = output average height bounced cm
20	_____________
25	_____________
30	_____________
35	_____________
40	_____________
45	_____________
50	_____________

3) Get a graph paper from your instructor. Trace the x-axis and the yaxis. and follow the steps.
A) Find the right scale for the x-axis and the y-axis.
(for example : 1 unit for x = 5 cm and 1 unit for y = 5cm)
B) Plot the points. Do not connect the dots.
C) Label the x-axis, don't forget the units (height dropped, cm)
D) Label the y-axis, don't forget the units (height bounced, cm)
E) give a title to your graph: height dropped vs height bounced.
F) With a ruler find the best-fit line. The line needs to go through the point (0,0)
(because, of course,  if height dropped = 0, height bounced = 0)
and the line needs to go through the cloud of points. Don't try to connect the dots.
It is ok if the line does not go through each dot. You are tracing the BEST FIT LINE.
G) show your instructor and write all these steps on a index card.

4) You are going to find the slope. The slope is the ratio between the rise and the run.
See the example below to understand how to find a slope and follow the steps below:

step1:
Trace a right angle in red in you graph
as shown here. Any triangle will work
but larger it is, more precise will be your
slope.

step2: rise = height of the triangle (cm)
run =base of the triangle (cm)

step3: find the ratio rise/run = ________
(there is no unit)

source:http://www.mathwarehouse.com/algebra/linear_equation/slope-of-a-line.php



4) your graph should be a line. This means that the relationship between the output (height bounced = y)
and the input (height dropped) is linear. Can you find the relationship between y and x ?
y = _____ x.

5) Now that you have found  the equation of the line, can you predict the value of y if x=32cm ?
(hint: plug x= 55cm in the equation y = m x, m is your slope). y predicted = ____________

6) Check with your graph if the predicted value makes sense . 
This is called interpolation.

GOING FURTHER : let's practice finding slope - try without hint. SLOPE = RISE/RUN

1) The top of the Leaning Tower of Pisa is about 55.9 meters above the ground. As of 1997 its top was leaning about
5.2 meters off-center. Approximate the slope of the tower.

(hint: slope = rise/run = height/base )

2) A ladder that hits the wall at a height of 12 feet with its base about 3 feet from the wall. Find the slope of the ladder.


3) on a website that advertises for skiing on the slopes of a volcano in Russia it is said:
(source: http://www.travelkamchatka.com/heliskiing.htm)
Avachinsky Volcano: flight time from PKC - 20 minutes,  2741 meters, height drop -
1700 meters, the length of run - 5-7 kilometers, steepness of slope is 25 - 35 degrees;
A) Can you find the slope of the volcano ? don't forget the convert km to m.

hint: rise= 2741m, run = 6000m about. find rise/run

 B) With a scale 1000m(in reality) = 1cm (on your paper) can you sketch the volcano ?
use a graph paper.

hint: trace a isocele triangle. the height is about 2.74cm and the base is 6x2 = 12cm

C) with a protractor find the angle between one leg and the base (see below).
Do you find the same angle described in the description?