1. Where the line cuts the coordinate axes Sunday, November 18, 2018 The Straight Line 1. Where the line cuts the coordinate axes Example The Graph drawn represents y = 4x + 8 Find the coordinates of A and B A B x y

The graph below is of 2x + 3y = 12 Workout the coordinates of A and B Example The graph below is of 2x + 3y = 12 Workout the coordinates of A and B

The gradient of a graph P2 y x Definition: The gradient of a straight line is the rate at which the line rises (or falls) vertically for every unit across to the right. Movement in y P1 Movement in x Movement in y Movement in x Gradient of line = Applications of Gradients Gradients are an important part of life. The roof of a house is built with a gradient to enable rain water to run down the roof. An aeroplane ascends at a particular gradient after take off, flies at a different gradient and descends at another gradient to safely land. Tennis courts, roads, football and cricket grounds are made with a gradient to assist drainage.

Example Find the gradient of the line which passes through A(2, 1) and B(7, 11) B(7, 11) y x 11 – 1 7 – 2 Gradient = 10 5 = A(2, 1) = 2 Note: The gradient of a line is positive when the line slopes upward as x increases

Find the gradient of a line which passes through (– 3, 7) and (1, – 5) Example Find the gradient of a line which passes through (– 3, 7) and (1, – 5) (– 3, 7) y x 7 – –5 – 3 – 1 Gradient = 12 –4 = = –3 (1, – 5) Note: The gradient of a line is negative when the line slopes downward as x increases

Example Obtain the gradient of the line which passes through the points (–1, –4) and (4, 6) y x (4, 6) 6 – –4 4 – –1 Gradient = 10 5 = = 2 (–1, –4)

Example Obtain the gradient of the line which passes through the points (–2, 8) and (5, 1) (–2, 8) y x 8 – 1 – 2 – 5 Gradient = 7 – 7 = (5, 1) = –1

The standard straight line Gradient of the line drawn Y- intercept (where it cuts the y axis)

Example Write down the gradient and value of the y intercept for each of the following graphs (a) y = 3x – 2 (b) y = 3 – x (c) 5x + y = 6 (a) Gradient = y- intercept = 3 – 2 (b) Gradient = y- intercept = –1 3 (c) Gradient = y- intercept = –5 6