Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Slope of a Line pages 353 - 357 of Understanding Maths Book 1 The slope of a line is a measure of how steep it is, or its gradient. Slope = Gradient = change in vertical height / change in horizontal length = rise/run (rise, rises to the top; run on your feet) Eg. If you rise 10 metres while walking 100m horizontally you have a slope of 0.1, and if you draw a triangle and ask Pythagoras, a walk of 100m and 50cm along that slope. Positive slope goes up right , negative slope goes down right. On a Cartesian plane (a graph) the slope between two points can be calculated from their coordinates. The two points are P(x1, y1) and Q(x2, y2) and the slope m, is m = (y2 – y1)/(x2 – x1) The slope between (1, 2) and (4, 5) = m = (5 – 2 )/(4 – 1 ) = 3/3 = 1 Note a vertical line does not have a slope as we can’t divide by zero. Exercise 18.5 on p.356 1a) -1, b) 3, c) 1, d) 2/3 = 0.667, e) -1, f) vertical, g) 0.6, h) 0. 2, 3 see attached sheet 4, 5, 8, 9 Two lines are parallel if their slopes are the same. 6 ,7 The opposite sides of a parallelogram are parallel, and hence have the same slope. 11 to 21, Substitute the numbers in the coordinates (2, 1) into the equation in place of x and y and then check it adds up to the number shown. 2 + 1 = 3. 22 to 31 This is a bit more awkward it means that if we have an equation of a line and know one of the coordinates of a point on the line we can work out the other. Remember the first position is the x coordinate and y is the second coordinate. So we get 22. (2, t) on 3x – y = 2, therefore 3*2 – t = 2, hence 6 – t = 2 or 6 – 2 = t and so t = 4.