1. Unit 28 Straight Lines Presentation 1 Positive and Negative Gradient Presentation 2 Gradients of Perpendicular Lines Presentation 3 Application of Graphs Presentation 4 Equation of Straight Line

2. Unit 28 28.1 Positive and Negative Gradient

3. A B Example Find the gradient of the line shown opposite. Solution -4-3-20123 5 4 3 2 1 -2 -3 -4 -5 y x ? ? ? ? Vertical change = 10 Horizontal change = 6 x y

4. A B Example Find the gradient of the line shown opposite. Solution x y -201234 5 4 3 2 1 A B (-2, 4) (4, 1) ? ? ? ? ? x y

5. Unit 28 28.2 Gradient of Perpendicular Lines

6. ? If two lines are perpendicular to one another, then the product of the two gradients is equal to -1. So if is the gradient of one line, the other line has a gradient of Example Show that the line segment joining the points A(3, 2) and B(5, 7) is perpendicular to the line segment joining the points P(2, 5) and Q(7, 3). Solution ? ? ? ? ? ? ? ? ? ?

7. Unit 28 28.3 Application of Graphs

8. Distance-time graph Distance Time The gradient gives the velocity. If the gradient is zero, the object is not moving. 2000 1500 1000 500 0 50100150200250300350400 Example The graph shows the distance travelled by a girl on bicycle. Find the speed she is travelling on each stage of the journey Solution ? ? ? ? ? ? ? ? ? A B C D E Time (s) Distance (m)

9. Solution The distance is given by the area under the graph, which can be split into 3 sections A, B and C Velocity Time velocity-time graph The gradient gives the acceleration. If the gradient is zero, the object is moving at a constant velocity. The area under this graph is the distance travelled. 8 7 6 5 4 3 2 1 2468101214 Example The graph shows how the speed of a bird varies as it flies between two trees. How far apart are the two trees? A B C 18m 36m 6m ??? ? ? ?? ? ?? Time (s) Velocity (m/s)

10. Unit 28 28.4 Equation of a Straight Line

11. The equation a of a straight line is usually written in the form Where m is the gradient and c is the intercept. Example (a) (b) Equation of line AB: As it passes through (3, 1) and 10 8 6 4 2 -3-20123456 A B G x y ? ? ? ? ? (-1, 9) (3, 1) ? ? ? ? ? ? ? ? ? O

12. 10 8 6 4 2 -3-20123456 A B G x y (-1, 9) (3, 1) (c) Coordinates of G: so (d) Equation of line through O, the origin, perpendicular to AB: Equation: i.e. (e) Equation of line through O, parallel to AB Equation: i.e. ? ? ? O ? ? ? ? ? ? ? ?