11 January 2022 110120 22 Level 6 Gradient
- Slides: 12
11 January 2022 11/01/20 22 Level 6 Gradient of a line segment LO: To calculate the gradient of a line segment. www. mathssupport. org
Gradient The gradient of a line is a measure of how steep the line is. The gradient is a comparison between vertical and horizontal movement. Find the gradient of this line. First we pick two points. 2 Find the vertical distance between the points. 3 Find the horizontal distance between the points. The gradient of this line is 3 2 www. mathssupport. org
Gradient The gradient of a line is a measure of how steep the line is. The gradient is a comparison between vertical and horizontal movement. Find the gradient of this line. First we pick two points. – 5 Find the vertical distance between the points. 2 Find the horizontal distance between the points. The gradient of this line is – 2 5 www. mathssupport. org
Gradient The gradient of a line is a measure of how steep the line is. The gradient is a comparison between vertical and horizontal movement. Find the gradient of this line. First we pick two points. 0 Find the vertical distance between the points. 5 Find the horizontal distance between the points. The gradient of this line is 0 = 0 5 The gradient of any horizontal line is 0, since the vertical step is 0 www. mathssupport. org
Gradient The gradient of a line is a measure of how steep the line is. The gradient is a comparison between vertical and horizontal movement. Find the gradient of this line. First we pick two points. Find the vertical distance between the points. 3 Find the horizontal distance between the points. The gradient of this line is 3 = undefined 0 The gradient of any vertical line is undefined www. mathssupport. org 0
Gradient The gradient of a line is a measure of how steep the line is. The gradient is a comparison between vertical and horizontal movement. Draw a line segment with gradient 1 3 First we plot one point. Measure the vertical distance from the numerator Measure the horizontal distance from the denominator 3 1 Now we plot the second point. Draw a line passing through the two points. www. mathssupport. org
The gradient formula If we want to calculate the gradient of any line. We need two points on the line. The coordinates of the points. Find the gradient of this line. x 2 – x 1 y 2 –y 1 0 A (x 1 , x 1 B (x 2 , y 2) y 1) x 2 y 2 –y 1 The gradient of the line AB is x 2 – x 1 www. mathssupport. org
Gradient Find the gradient of the line segment joining the points. (2 , 5) and (4 , 11) 20 Gradient = y 2 –y 1 x 2 – x 1 = 11 – 5 4 – 2 15 5 -2 0 Gradient (4 , 11) x 2 y 2 10 (2 , 5) x 1 y 1 0 -5 www. mathssupport. org 2 4 6 Gradient =3
Gradient Find the gradient of the line segment joining the points. (4 , 0) and (1 , 15) 20 = y 2 –y 1 x 2 – x 1 Gradient = 15 – 0 1 – 4 Gradient = -5 Gradient (1 , 15) x 2 y 2 15 10 5 0 -2 0 -5 www. mathssupport. org 2 (4 , 0) x 1 y 1 4 6
Gradient Find the gradient between each pair of points. Leave your answer as a fraction where appropriate. ① ② A(4 , – 2) B(7 , 7) Gradient ③ = B(3 , – 1) 3 B(– 1 , 4) = www. mathssupport. org Gradient ④ A(2 , 6) Gradient A(1 , 9) = – 5 A(4 , – 2) B(7 , – 3) 2 3 Gradient = 1 – 3
Gradient �The gradient tells us how steep a line is �It can be calculated using one of the following formulae given two co-ordinates (x 1 , y 1) and (x 2 , y 2) www. mathssupport. org
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