To find the gradient of a line from its graph, we first need to know what gradient means.

In simple words, the gradient (or slope) shows how steep a line is. It looks at how much the line goes up (rise) compared to how much it goes sideways (run).

You can calculate the gradient using this formula:

$$m = \frac{\text{rise}}{\text{run}}$$

Steps to Calculate the Gradient

1. Pick Two Points on the Line:
   Find two clear points on the line. For example, let’s use points ( A(2, 3) ) and ( B(5, 7) ).

2. Find the Coordinates of the Points:
   The coordinates help us understand the changes. For point ( A ), the coordinates are ( (x_1, y_1) = (2, 3) ) and for point ( B ), they are ( (x_2, y_2) = (5, 7) ).

3. Calculate the Rise and Run:
   To find the rise, subtract the y-coordinates:

   $$\text{rise} = y_2 - y_1 = 7 - 3 = 4$$

   To find the run, subtract the x-coordinates:

   $$\text{run} = x_2 - x_1 = 5 - 2 = 3$$

4. Use the Formula for Gradient:
   Now that we have the rise and run, we can find the gradient:

   $$m = \frac{4}{3}$$

   This tells us that the line goes up 4 units for every 3 units it goes sideways.

Conclusion

When you look at a graph, just pick two points and use this easy calculation.

Remember:

• If the gradient is positive, the line goes up as you move from left to right.
• If it’s negative, the line goes down.
• If the gradient is zero, the line is flat.
• If the gradient is undefined, the line goes straight up.

Now you're ready to find gradients from graphs with confidence!