1. 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

2. 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

3. 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.

4. 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

5. 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

6. 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)

7. 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

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

9. 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