Graphing and equations How to take data from the table to the graph to the equation, with all the bells and whistles

Graphing data Make your graph take up plenty of room on the axis. No tiny graphs! Each axis gets a label (for example: “Distance”) and a unit (for example: “meters”) like this: D (m) or t (s) Mark the points with dots or x A best-fit line or curve gets as close as possible to all the points you measured.

Graph this information: When you measure the distance your car can travel compared to what volume of gas it takes, you get this data. On your paper, make a graph of -distance (vertical) vs. volume (horizontal). Be sure to label the axes and make a best fit line. Volume (gallons) Distance (miles) 1.2 40 3.7 130 9.7 365 15.3 540

Making an equation Using the form y = mx + b, substitute the information from your graph for each of the variables in the equation. y is the label of the vertical axis m is the slope (keep the units in when you calculate). x is the label of the horizontal axis b is the point where the line intercepts the vertical axis.

The equation: D = 35.9 miles/gallon (V) + 0 miles You don’t really have to put in the 0 miles, but I added it so you’d notice that it had a unit.

Now try this data – graph and equation You measure the growth of a tree for several years. Here is the length of the tree at each time. Time (years) length (meters) 2.7 1 5.0 2 7.3 4 11.9 6 16.5

L = 2.3 m/yr (t) + 2.7 m The equation: Notice that there are six things that have to be right to get the right equation. If you’ve done it correctly, you could make the graph completely from the equation.

Try this: An elevator is moving down. Taking the height of the main floor to be zero, graph and make an equation for this data. Time (s) Height (m) 45 1 30 2 15 3 4 -15

The equation (was yours 100% correct?) H = -15 m/s (t) + 45 m