What is a gradient?

The gradient of a line is the slope of the line. Gradient is defined as vertical rise/horizontal run. It is denoted by the letter m, where m = (y1-y2)/(x1-x2). (x1,y1) and (x2,y2) are any two points on the line. For any line, we can also draw a right-angled triangle to measure the gradient of the line. See the following diagram.

Two methods to calculate gradient, m

• Method 1
  • Use the formula m = (y1-y2)/(x1-x2)
• Method 2
  • Draw a right-angled triangle (see diagram above)
  • Find the vertical rise (y2 – y1) [Measuring the vertical distance]
  • Find the horizontal run (x2 – x1) [Measuring the horizontal distance]
  • Calculate the gradient = vertical rise/horizontal run

Question: Is the formula m = (y1-y2)/(x1-x2) and m = (y2-y1)/(x2-x1) the same?

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