M3.9.6 For the adult
Steepness: the gradient
How steep is a line? Can I put a number on it?
What this chapter teaches
The gradient of a line is how steep it is: the rise divided by the run, between any two points on it. A line that goes up to the right has a positive gradient, and a line that goes down has a negative one. In a rule like y = 2x + 1, the 2 is the gradient.
Three questions to ask
There is no one right wording. Listen for the idea.
- How do you find the gradient of the line through (1, 2) and (3, 8)?
- Why is the gradient negative when the line goes down to the right?
- In y = 4x − 3, which number is the gradient?
After the chapter, the learner can
- Find the gradient of a line from two points on it
- Say how the number in front of x changes the line
What they copy into their notebook
Gradient = rise ÷ run. A line going up to the right has a positive gradient. A line going down has a negative one. In y = mx + c the number in front of x is the gradient.