Use the BACK button on your browser to return to the main text document

NAME ______________________________

Now that we have graphed our data, what next? Our next goal is to examine how we can use our graphs to make predictions. Such procedures are used in every area of study, from medicine to the business world. For example, a pediatrician, needs to be able to predict the normal height and weight of an infant from its age by simply looking at a growth chart. Using our graphs can we predict how high people can jump?

This handout will be done step-by-step as a class. However, you are responsible for you own work. Each of you will come out with slightly different results-AND THAT'S OK!

PART I:

1. DRAWING THE BEST FIT LINE

Find a line that captures the general appearance of the data. The line should run approximately through the middle of your scatter.

2. PREDICTING FROM YOUR BEST FIT LINE

Your line is a model for the relationship between reach height and jump height. We can use this model to estimate how high you can jump. Find your reach height on the horizontal axis and move upward until you come to the line. Than move to the left until you come to the vertical scale. Read your predicted jump height.

WRITE DOWN THE JUMP HEIGHT THAT WAS PREDICTED __________________

How does this predicted jump height compare with your actual jump from the data you collected? What does this imply about your best fit line?

PART II: PREDICTING FROM AN EQUATION OF A LINE

So far, you've used your graph to predict your jump height and compared it to what actually happened. However, how would you go about trying to predict someone's jump height if it goes beyond your graph? The next stage will be taking graph prediction one step further by using equations. The equation of a line is y = mx + b. This means nothing to you right now, but let's break each variable down and explore how it is this very equation that will allow you to predict jump heights for anyone!

3. FINDING THE SLOPE OF YOUR LINE

Slope can be interpreted as a rate of change. According to our graph, the slope will measure the rate of change in jump height as compared to reach height. In other words, how much more will someone's jump height increase as their reach height increases? For example, let's say the slope came out to be 2.5 inches (a complete guess). This would mean that for every one inch increase in reach height, the jump height would increase 2.5 inches.

Here are a couple of ways to interpret slope as it applies to your graph:

slope = change in vertical distance/change in horizontal distance

OR

slope = rise/run

OR

slope = (y₂-y₁)/( x₂-x₁) Using points (x₁, y₁), (x₂, y₂)

CHOOSE 2 POINTS FROM YOUR LINE: They do not need to be points from your data. Make sure they are fairly far apart.

From this point you can work off your graph to calculate the distance vertically and horizontally or you may proceed algebraically:

Use the points to find the slope from this equation:

slope = (y₂-y_{1) / (}x₂-x₁)

Slope can be defined by the letter (m).

THE SLOPE OF YOUR LINE IS ___________________

ACCORDING TO YOUR DATA THE SLOPE MEANS___________________________________________________________________________________________________________________________

4. USING THE SLOPE TO FIND THE Y-INTERCEPT

The y-intercept is the value of (y) when x is 0. It is where your line will cross the y axis. In terms of our example, our (x) variable represents reach height. Therefore, our y-intercept would be the height of our jump at 0 reach height! Sounds obvious-huh!!! In our example this may not be 0. It could be a negative number-which still would make sense mathematically. Sometimes you will be unable to see where the line crosses the y-axis because your graph is too small. Let's see how we can find the y-intercept algebraically.

Your slope is _________________

Choose one pair of your points from #3 __________________

Use the following equation of a line:

From the above you should have a value for x, y and slope. Plug in the points and solve for the y intercept.

SHOW YOUR WORK HERE

YOUR Y INTERCEPT IS ____________________________________

5. PUT IT ALL TOGETHER

You now have all the variables you need for the equation of a line. They are:

• slope which is noted as the letter (m)
• y-intercept which is noted as the letter (b)
• y-which is any value for the jump height
• x- which is any value for the reach height

YOUR EQUATION IS:_____________________________________________

6. PREDICTING FROM THE EQUATION

You can predict from your jump height using the equation. Your jump height will be the variable (y). Just place your height in for x, along with your slope and y-intercept and solve for (y).

SHOW YOUR WORK HERE

YOUR PREDICTED JUMP HEIGHT IS ________________________

How close is your predicted jump height to your real jump height?

_________________________________________________________________________________________________________________________________________

7. COMPARE WITH CLASS RESULTS

Let's take some time out to compare your results with those of other students. Whose line did the best job for coming closest to their actual jump height?

8. PREDICT A CLASSMATE'S JUMP HEIGHT

As you did for your own jump height in step 6, let's predict someone else jump height.

SHOW YOUR WORK

9. EXERCISE

The tallest living woman is Sandy Allen at 7ft, 7 inches. Now use the above steps to predict her jump height.

Use the BACK button on your browser to return to the main text document