Finding the gradient is a very common task that you meet while doing practicals and analysing data.

The gradient, m, can be calculated by the formula

$$ m={{change\ in\ the\ y\ axis} \over {change\ in\ the\ z\ axis}} $$

This is how it’s done:

  • Find any two points on the line that are far apart. The points must fall on the line but they don’t have to be an actual data point that you plotted previously
  • Label your points P1 with coordinated \((x_1, y_1)\) and P2 with coordinates \((x_2, y_2)\)
  • Use the equation \(m = {(y_2 – y_1) \over (x_2 – x_1)} \)
  • Write the appropriate units

Example

Here is an example using the graph of the best fit straight line of the previous topic.

Best fit line 1 cropped gradient

\( m = {(8.0 – 1.0) \over (1.925 – 0.300)}  \)

\( m = {7.0 \over 1.625} \)

\( m = 4.3 \)

To write the appropriate units, consider what quantities you are dividing. In this case, the quantity on the y axis is period2 with units s2 while the quantity on the x axis is length with units m. So when I wrote \( m = {7.0 \over 1.625} \) in the line above, I could have added the units like this to make it more accurate $$ m = {7.0  \over 1.625} {s^2 \over m} $$ and then finally write the gradient as $$ m = 4.3 {s^2 \over m}$$ or $$m = 4.3\ {s^2 m^{-1}}$$.

When finding the gradient always find out the units and write it as a part of your answer.