Gradient (Slope) of a Straight Line
The Gradient (also called Slope) of a line shows how steep it is.
Calculate
To calculate the Gradient:
Gradient = \frac{Change in Y}{Change in X} |
Have a play (drag the points):
Examples:
The Gradient = \frac{3}{3} = 1 So the Gradient is equal to 1 |
The Gradient = \frac{4}{2} = 2 |
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The line is steeper, and so the Gradient is larger. |
The Gradient = \frac{3}{5} = 0.6 |
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The line is less steep, and so the Gradient is smaller. |
Positive or Negative?
Going from left-to-right, the cyclist has to Push on a Positive Slope:
When measuring the line:
- Starting from the left and going across to the right is positive
(but going across to the left is negative). - Up is positive, and down is negative
Gradient = \frac{−4}{2} = −2 |
That line goes down as you move along, so it has a negative Gradient.
Straight Across
Gradient = \frac{0}{5} = 0 |
A line that goes straight across (Horizontal) has a Gradient of zero.
Straight Up and Down
Gradient = \frac{3}{0} = undefined |
That last one is a bit tricky ... you can't divide by zero,
so a "straight up and down" (vertical) line's Gradient is "undefined".
Rise and Run
Sometimes the horizontal change is called "run", and the vertical change is called "rise" or "fall":
They are just different words, none of the calculations change.