Linear functions
- 1. 1 Sep 2303:21 p.m. Linear functions During this lesson we will : • Explore the equation of a straight line. • Discover algebraic relations between pairs of parallel and perpendicular lines. • Explore the absolute value function and its properties. • Recognise and draw piecewise linear functions.
- 2. 2 Sep 2303:21 p.m. Distance between two points A B
- 4. 4 Sep 2303:21 p.m. Linear functions The graph is a straight line.
- 5. 5 Sep 2303:21 p.m. Gradient of a line The gradient of a line is a measure of its steepness If and positive gradient negative gradient
- 6. 6 Sep 2303:21 p.m. horizontal lines have a gradient of 0 (zero) vertical lines have an undefined gradient parallel lines have equal gradients the gradients of perpendicular lines are negative reciprocals if the gradients are m1 and m2 then: or
- 7. 7 Sep 2303:21 p.m. Equations of lines The equation of a line is an equation which states the connection betwen the x and y values for every point on the line. All vertical lines have equations of the form x = a , ( a is a constant) All horizontal lines have equations of the form y = c , ( c is a constant) slope-intercept form or explicit form gradient y-intercept general form or implicit form (not a function)
- 8. 8 Sep 2303:21 p.m. Write down the gradient and y-intercept of these straight lines: y = 5x 2 2y = 1 6 x 3x + 2y 8 = 0
- 9. 9 Sep 2303:21 p.m. Sketch the graphs of these equations: y = 2 x 1 3y + 2x 3 = 0 2y x + 1 = 0
- 10. 10 Sep 2303:21 p.m. Write down the equation of the straight line which passes through the points A (2,5) and B (6,17).
- 11. 11 Sep 2303:21 p.m. Find the explicit and implicit equations of the line through (-1,3) with a slope of 5.
- 12. 12 Sep 2303:21 p.m. Are L1 with equation 2x y + 2=0 and L2 with equation x + 4y 1 = 0 perpendicular lines?
- 13. 13 Sep 2303:21 p.m. Find the equation of the line through (1,-5) and (5,-2). Express the equation in the form Ax+By + C = 0, with A, B and C integer numbers.
- 14. 14 Sep 2303:21 p.m. Intercepts xintercept yintercept x y The x-intercept is found by letting y =0. The y-intercept is found by letting x=0.
- 15. 15 Sep 2303:21 p.m. For the line with equation 2x - 3y =12, find axis intercepts.
- 16. 16 Sep 2303:21 p.m. Find the point of intersection of the lines : 3x+4y=29 and 2x 5y=4 3x+4y=29 2x 5y=4
- 17. 17 Sep 2303:21 p.m. At the end of the lesson: Reproduce exactly this drawing on your GDC.
- 18. 18 Sep 2303:21 p.m. At the end of the lesson: Reproduce exactly this drawing on your GDC.
- 19. 19 Sep 2303:21 p.m. Can you give a formula for the following graph?
- 20. 20 Sep 2303:21 p.m. Piecewise linear functions Draw the graph of:
- 25. 25 Sep 2303:21 p.m. Absolute value function (Modulus) Sketch the graph of f(x).
- 27. 27 Sep 2303:21 p.m. With calculator: Menu graph OPTN Num (F5) Abs (X) Casio TI-84 Y= MATH > 1 (X )