1. BASIC GRAPHS Physics with Technology

2. Scatter Plot  When doing a lab, we often graph a series of points. This is called a scatter plot. Scatter plot

3. Best Fit Line  Using the dots on our scatter plot as our guide we then draw a solid line that follows the data. This is called a best fit line. ← best fit line

4. Label and Units Review  When preparing a graph it is important to remember that both axes should ALWAYS have a label and units.  Remember that we write labels and units like this:  Label (units)  Here are some examples:  Temperature (ºC)  Time (s)  Length (cm)

5. Scale Review  It is also important to use an appropriate scale. The scale is how much each gridline is worth.  For example, the x-axis gridlines might count by twos while the y-axis gridlines count by tens.  As a general rule of thumb, the final graph you draw should use more than half of each axis.  This means that if your largest x-value is only 5 then don't use a scale that goes all the way to 100.

6. In Real Life  In math class you are used to dealing with perfect graphs that form perfect lines or perfect curves. Each point is exactly where you expect it to be.  This simply doesn't happen in real life. In real life there is natural variation. There is human error.  In real life graphs do not form perfect shapes.  Because of this it is OUR job (as scientists) to decide what shape the graph is closest to. The answer is often (but not always) a straight line.

7. Best Fit Rules If a scatter plot appears to be following a straight line trend, then it is time to draw a BEST FIT line to go with it. There are three rules you must remember. 1.Your line will NOT be able to touch every dot in the scatterplot. Instead you must draw your line through the center. This means that the number of dots above your final line should equal the number of dots below your line. 2.In order to calculate a valid slope it is important that the line you draw is PERFECTLY STRAIGHT. This means that you must always use a ruler or straight edge when drawing your line. (A best fit line is never squiggly or bent!) 3.Sometimes your first attempt is not as good as it could have been. And it is important that your final graph is as accurate as is humanly possible! This means that if your first graph is obviously NOT the BEST fit you need to erase it and try again. Ask yourself a few basic questions. Would rotating my line a little bit get me closer to more dots? Would sliding my line up, down, or sideways help? If the graph is obviously flawed then it isn't good enough.

8. Note:  It is important to realize that not all graphs are straight. It is ok to curve.  If your graph is obviously curving in one direction then let it curve. Just sketch a best fit curve by hand and don't worry about perfection.  Now use a ruler and draw a best fit line for the scatter plot you have been given in your notes packet.

9. The Importance of (0,0)  The point (0,0) can be very important to a graph because it can force a graph to curve.  We will learn more about this point and how to use it.

10. Warnings Finally, there are some warnings. The following are some common mistakes. Watch out for these! 1.Do NOT just connect two dots and call it a best fit. A best fit line is NOT a game of connect the dots. The objective is to draw a line that gets as close to as many dots as possible.

11. Warnings 2.Always start your scale with 0.  Sometimes students will "zoom in" on their graph by starting their corner grid with something besides zero.  Let's say your data set was [12, 14, 18]. You might think it would be a good idea to make your axis start on 10 and end on 20.  Don't!!!  There is nothing wrong with it mathematically, but it will totally mess up the data analysis that we are going to use later.

12. Warnings 3.Keep your scale consistent.  Sometimes students set up their horizontal axis like this: 0 → 1 → 1.1 → 1.2 and so on.  Can you spot the mistake?  The first interval (from 0 to 1) was a LOT bigger than the second interval (from 1 to 1.1)  Be careful! This is an easy mistake to make.

13. 4 Basic Relationships & Shapes  It is important to realize that best fit "lines" are not always lines.  In fact, a straight line is only one of our possibilities.  You must be able to identify all four of the basic shapes we will encounter this year.  Each type of graph represents a different type of relationship between the independent and dependent variables.

14. Line  The most common shape for a graph is a straight line.  If we see this shape, we say that the variables are directly proportional (relationship) and that the shape is a line.  The phrase that best describes this type of system is, "As the independent variable got bigger the dependent variable got bigger too."  The important idea to remember is that both variables do the same thing. Some Real World Examples: The more I eat the more I weigh. The less I study the less points I get on quizzes. The more time I work the more money I get paid.

15. Hyperbola  If we see this shape, we say that the variables are inversely proportional (relationship) and that the shape is a hyperbola.  The phrase that best describes this type of system is, "As the independent variable got bigger the dependent variable got smaller."  The important idea to remember is that the variables do opposite things. Some Real World Examples: The more I exercise the less time it takes to run a mile. The less I study the more classes I fail. The more I practice the less mistakes I make.

16. Parabola  If we see this shape, we say the variables have a quadratic relationship and the shape is a parabola.  The phrase that best describes this type of system is, "As the independent variable got bigger the dependent variable got WAY bigger." (Very scientific, I know.)  The important idea to remember is that instead of having a constant slope like a line, a parabola keeps getting steeper and steeper as you move forward.

17. Root  If we see this shape, we say the variables have a root relationship and the shape is a hill. (This is a shape name your teacher made up, so don't try to quote it in college, no one will know what you are talking about.)  A hill is actually a parabola lying on its side.  As one variable gets bigger the other variable.... doesn't do as much as you would expect.  The phrase that best describes this type of system is, "As the independent variable got bigger the dependent variable got a LITTLE bigger."  The important idea to remember is that instead of having a constant slope like a line, a hill keeps getting less steep as you move forward. At the top it is almost flat.

18. Practice  Now it is your turn to practice by completing the graphs lab in your notes packet. (No full lab write up.)  Graphs lab can be found at tinyurl.com/graphLab2  You will need to check out your Chromebook  To log onto your Chromebook you put in your school email which is your Skyward login with all the numbers @alpineSD.org  Your password, if you have not changed it, is ASD and your Birthday: mm/dd/yyyy