Gradient between two pointsThe gradient of a line is the slope of the line. The gradient is the ratio of the rise to the run of the line.We use the letter m for gradient.

(x1, y1)

(x2, y2)

x

y

(y2 y1)

(x2 x1)

For any line.

Pick 2 points (x1, y1) and (x2, y2).

Draw a right angled triangle

Then use rise over run

Gradient between two pointsThe gradient of a line may be small, having a “gentle” slope

The gradient of a line may be large, having a “steep” slope

A line with a positive gradient slopes “upwards” from left to right.

A line with a negative gradient slopes “downwards” from left to right.

Example 1Show the points A(2, 5), B(6, 11) and C(–6, –7) are collinear.Remember collinear means the points lie on the same line.First calculate the gradient of any 2 points, say AB.

Then calculate the gradient of either A or B and C.

As mAB = mAC A, B and C are collinear.

What would happen if we had the points the other way around?.

Today’s work

Exercise 7.3Page 279Q1 a→cQ2, 5, 6 & 12