Gradient between two points The 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. (x 1, y 1 ) (x 2, y 2 ) x y (y2  y1)(y2  y1) (x2  x1)(x2  x1) For any line. Pick 2 points (x 1, y 1 ) and (x 2, y 2 ). Draw a right angled triangle Then use rise over run

Gradient between two points The 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 1 Show 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 m AB = m AC A, B and C are collinear. What would happen if we had the points the other way around?.

Today’s work Exercise 7.3 Page 279 Q1 a→c Q2, 5, 6 & 12