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

Radar sends out a wave that bounces off an object then returns to the radar. The radar is able to determine the distance an object is away from it at a given time. The radar takes several readings at slightly different times to calculate the speed of an object. If these readings were graphed on a time-distance graph, they may look like these: Equations of Lines

1. Which graph shows jets that are moving away from the radar. 2. Which jet is going the fastest? Why? 3. Which jet was the farthest away from the radar when the timing started? 4. Draw a graph of a helicopter that is hovering 100 yards away from the radar. Equations of Lines

The coordinates x and y of any point on a line L are linked by an equation, called the equation of the line If a point Q lies on a line L the the coordinates of Q satisfy the equation of L Equations of Lines The equation of a straight line can be written in the form: m = slope c = the y-intercept (the point where the line crosses the y-axis y = mx +c is called the gradient-intercept form y = mx + c

Equations of Lines The slope is ½. It crosses the y-axis at 1. Using y = mx +c, then: Consider the following line:

Consider y = 2x – 3 xy Equations of Lines

Finding the Equation of a Line Find the equation of the line that has a gradient of and passes through the point (2, 3). Give you answer in gradient – intercept form. 2(y – 3) = 1(x – 2) 2y – 6 = x – 2 y = ½ x + 2

1) Find, in gradient-intercept form, the equation of the line that passes through (10, 0) with a gradient of 2/5. Practice 2)The line L has gradient 1/3 and passes through A (2, -1) a) Find the equation of line L in gradient-intercept form. b) Write down the point of intersection of line L with the y-axis. c) Find the point of intersection of L with the x-axis. d) Draw the line L, clearly showing the information from (b) and (c). y = 2/5x - 4 y = 1/3x - 5/3 (0, -5/3)(5, 0)

Equations of Lines ax + by + c = 0 x – 2y + 2 = 0

1) Find, in general form, the equation of the line with gradient -3/4 and passing through (8, -7). Practice 2) Find, in the general form, the equation of the line which passes through the points F(1, 1) and G(2, 4) 3) Find the gradient of the line 5x – 3y – 15 = 0. 4) Does (-4, 1) lie on the line with equation 2x + y – 5 = 0? 5) Line L joins the points A (-3, 5) and B (1, 2). - Find the equation of the line in the general form. - The Point Q (5/3, t) lies on L. Find the value of t. 4y + 3x + 4 = 0 y - 3x + 2 = 0 5/3 no 4y + 3x - 11 = 03/2

Consider the line that has a gradient of and passes through the point (2, 3). Gradient-intercept formGeneral Form Practice y = ½ x + 22y - x - 4 = 0

Find the equations of the line with graphs. Practice y = 2/3x - 6y = -1/6x - 2