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How to find Gradient of Straight Lines

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1. 1. x y y = 2x - 3 Images and Clipart from Google Images
2. 2. Gradient represents how steep a slope is : Uphill is Positive, and Downhill slopes are Negative. The Gradient symbol is “m” for how “mountainous” a slope is. Rene Descartes invented Gradient, and assigned the letter “m” as “montagne”, which is French for Mountain.
3. 3. As we go up the mountain, it becomes steeper. (Positive Increase) As we go up the mountain it gets cooler, with progressively less soil and plants. (Negative Decrease, downhill graphs). Distance up Mountain Steepness Distance up Mountain Temperature Distance up Mountain Soil&Vegetation
4. 4. There are four types of “Gradient” or “Slope” Images Purchased from Photozone.com
5. 5. m = UP = 2 ACROSS 2 RUN Across = 2 RISE Up = 2 The “Gradient” or “Slope” is measured as how far UP we have gone, compared to how far we have gone ACROSS. = 1 Cycling Image Purchased from Photozone.com
6. 6. 5 -5 The “Gradient” or “Slope” between two points is how far UP we have gone, compared to how far we have gone ACROSS. m = RISE RUN or m = Change in Y Change in X A B RUN Across = 4 RISE Up = 8
7. 7. 5 -5 The “Gradient” or “Slope” between two points is how far UP we have gone, DIVDED BY how far we have gone ACROSS. m = RISE RUN m = 8 4 m = 2 A B RUN Across = 4 RISE Up = 8
8. 8. Step 1 - Have two points that are on a straight line Step 2 - Work out the Vertical and Horizontal Distances Step 3 - Substitute the Step 2 values into the Gradient Slope formula: Step 4 - Reduce Down Fraction Answers to simplest form Step 5 Write Gradient Slope value as Positive for Uphill and Negative for Downhill. m = RISE (Vertical Change) RUN (Horizontal Change)
9. 9. B 5 -5 Find the Gradient between points “A” and “B”. The “Gradient” or “Slope” between two points is how far UP we have gone, DIVIDED BY how far we have gone ACROSS. A
10. 10. B 5 -5 Find the Gradient between points “A” and “B”. We create a Right Angled Triangle around the points, and work out the Vertical RISE, and the Horizontal RUN values. A RUN Across = 7 RISE Up = 3
11. 11. B 5 -5 Find the Gradient between points “A” and “B”. A RUN Across = 7 RISE Up = 3 m = RISE RUN m = 3 7 m = 3/7 (Uphill Positive Gradient)
12. 12. D 5 -5 Find the Gradient between points “C” and “D”. The “Gradient” or “Slope” between two points is how far UP or DOWN we have gone, DIVIDED BY how far we have gone ACROSS. C
13. 13. D 5 -5 Find the Gradient between points “C” and “D”. We create a Right Angled Triangle around the points, and work out the Vertical RISE, and the Horizontal RUN values. C RUN Across = 6 RISE Up = 4
14. 14. D 5 -5 Find the Gradient between points “C” and “D”. C RUN Across = 6 RISE Up = 4 m = RISE RUN m = 4 6 m = 4/6 = - 2/3 (Downhill Negative Gradient)
15. 15. E F 5 -5 Find the Gradient between points “E” and “F”. These two points are at the same Height, and so the RISE = 0. m = Rise / Run = 0/7 = 0 RUN Across = 7 RISE Up = 0
16. 16. F B Parallel Lines always have Identical Gradient Slopes Two lines which go in the exact same direction, have the exact same Gradient, and stay the same distance apart forever. AB // EF A RUN = 7 RISE = 3 E RUN = 7 RISE = 3
17. 17. F B Perpendicular Lines have Negative Inverse Gradients Two lines which cross at 90 Degrees to each other, have Negative Reciprocal Slopes: mAB = 3/7 and mEF = -7/3 AB _ EF A RUN = 7 RISE = 3 E RUN = 3 RISE = 7
18. 18. Blank X-Y Grid -3 3 5 -5
19. 19. http://passyworldofmathematics.com/