Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004 AND Mathematical Studies Standard Level Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman Oxford University Press, 2012

Slope of a line is the __________, of the line. steepness Gradient of a Line

Slope can be ________, ________, or ______. It is also possible for slope to ___________. zeropositivenegative not exist Gradient of a Line

The gradient tells you the rate. Distance (m) Time (s) Every second this object travels 1 m. Hence, its rate is 1 m/s Every second this object travels 2 m. Hence, its rate is 2 m/s The steeper the gradient the greater the rate

To determine slope you need to know how far the line ______ and how far the line ______. “runs” “rises” slope = m = Gradient of a Line

Determine the slope of each line. 1)2) Practice 1

x1x1 x2x2 x 2 - x 1 If A (x 1, y 1 ) and B (x 2, y 2 ) ate two points that lie on a line L, then the gradient of L is m = Gradient of a Line A B L

Find the slope of the line through the points: a) (1, 6) and (3, -2) b) (7, -6) and (-5, -2) c) (4, 3) and (7, 3) d) (-2, 5) and (-2, 8) Practice a) -4 b) -1/3c) 0d) undefined

(-1, 2) and ( 2, 2) (3, 4) and (3, 1) Remember Horizontal Line: m = 0 Vertical Line: m = undefined

Draw a line through (-2, 1) with a gradient Practice

A line with a positive slope (m > 0) ____ from left to right A line with a negative slope (m < 0) ____ from left to right A line with zero slope (m = 0) is ________ A line with undefined slope is _______ rises falls horizontal vertical a b d c Gradient of a Line

Parallel and Perpendicular Lines Two lines are parallel if they have the same gradient. Two lines are perpendicular if their gradients are opposite reciprocals or if the product of their gradients is -1.

If a line has gradient find the gradient of all lines: a)parallel to the given line b)perpendicular to the given line Practice a) 5/3b) -3/5

Line L 1 passes through points A (0,-3) and B(-7,4): a) find the gradient of L 1 b) draw and label L 1 c) draw and label a second line L 2 passing through the origin and parallel to line L 1 Practice a) -1

Find a given that the line joining M(3, a) and N(a, 5) has a gradient of Practice a) 9

Find t given that the line joining A(-1, -3) to B(4, t) is perpendicular to a line with gradient Practice a) -5