Distance/Time Graphs

Distance time graphs is a visual way to show a collection of data. It can help understand the relationship between the data.
In a distance time graph, the x axis is the independent variable (component you can change--in other words it is not fixed) and shows time in seconds. On the y axis, it shows distance in meters, and it is the dependent variable (component you cannot change--in other words, it is fixed).
If the points on a line graph do not form a straight line, a line of best fit must be drawn in.


TO FIND THE SLOPE (SPEED) OF A LINE:

The slope of a line determines the speed. The higher the slope the greater the speed but if the slope is low, the speed is also low.

In other words, if the slope is high, then the speed is great. If the slope is low, the speed is low. 

Equation for a line: y = mx + b
m is the slope of the line,
b is the y intercept of the line
y is the dependent variable, on the y axis (distance).
x is the independent variable, on the x axis (time).


In a distance/time graph the equation changes from 


y = mx + b to d = v / t


d is the dependent variable (distance)
t is the independent variable (time)
v (speed) is the slope of the line.

We can find the slope of a line by using maths which says to find the slope, we have to divide rise over run.
To find the slope using the v = d/t formula we do this,
d (the slope (speed)) is = to the change in distance (on the y axis) / the change in time (on the x axis).
basically:
slope = rise/run or v = d/t

The slope of a line is calculated as follows:
For example...
d = d1 - d2      (because we are calculating the change in distance, and from d1 - d2, we calculate the change in distance by subtracting--which we need change in distance for the equation.)
  = (insert number here) meters
t = t1 - t2         (remember, we are finding out the change of the time this time, so we can divide it with the distance to get the slope to find the speed).
 = (insert number here) seconds
Then finally, get both calculations and put it into the equation:
v = d / t
It will equal v = (insert number here) m/s (meters over seconds)

Note: it does not have to be in m/s if a graph says in the dependent axis kilometers and on the independent axis minutes the result of the slope will be v=(insert number here)km/min.

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