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Gradient between two points

y. x. ( y 2  y 1 ). ( x 2 , y 2 ). ( x 2  x 1 ). ( x 1 , y 1 ). 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. For any line.

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Gradient between two points

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

  2. 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.

  3. 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. What would happen if we had the points the other way around?. As mAB = mAC A, B and C are collinear.

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

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