Part 04 · Graphs · Card 2 of 8
Gradient
How steep a line is. It is the amount the line goes up for every 1 step across.
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Analogy
Like the slope of a hill: a bigger number means a harder climb.
Example
Points (1, 2) and (5, 10)
Up = 10 - 2 = 8Across = 5 - 1 = 4Gradient = 8 / 4 = 2
In practice
A road sign saying 10% gradient means the road rises 10 metres for every 100 metres across.
Practice
Flashcards
- What is the gradient between (1, 2) and (5, 10)?2. The line rises 8 over a run of 4.
Interview questions
- Find the equation of the straight line through (0, 3) and (2, 7).
- Gradient = (7 - 3) / (2 - 0) = 2
- The line crosses the y-axis at 3
- So y = 2x + 3
- Check that (2, 7) fits: 2 x 2 + 3 = 7
Questions people ask
How do you calculate gradient from two points?
Divide the change in y by the change in x. Subtract the y values and the x values in the same order. Between (1, 2) and (5, 10), the change in y is 8 and the change in x is 4, giving a gradient of 2.
What does a negative gradient mean?
A negative gradient means the line goes downhill when you read it from left to right. For every step across, the line drops. A gradient of -3 means the line falls 3 units for each 1 unit across. A zero gradient is a flat horizontal line.