All straight lines can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. Alternatively, lines can be written in the general form of Ax + By + C = 0, where A, B, and C are integers or surds. Lines parallel to the x-axis have the form y = c, where c is a constant. Lines parallel to the y-axis have the form x = k, where k is a constant. The example shows finding the equation of a line perpendicular to another line in general form.

1. Equation of Lines
(Linear Function)

2. Equation of Lines
(Linear Function)
All straight lines can be written in the form;

3. Equation of Lines
(Linear Function)
All straight lines can be written in the form;
y  mx  b

4. Equation of Lines
(Linear Function)
All straight lines can be written in the form;
y  mx  b
m  slope

5. Equation of Lines
(Linear Function)
All straight lines can be written in the form;
y  mx  b
m  slope
b  y intercept

6. Equation of Lines
(Linear Function)
All straight lines can be written in the form;
y  mx  b
m  slope
b  y intercept
OR

7. Equation of Lines
(Linear Function)
All straight lines can be written in the form;
y  mx  b
m  slope
b  y intercept
OR
Ax  By  C  0

8. Equation of Lines
(Linear Function)
All straight lines can be written in the form;
y  mx  b
m  slope
b  y intercept
OR
Ax  By  C  0 (general form)

9. Equation of Lines
(Linear Function)
All straight lines can be written in the form;
y  mx  b
m  slope
b  y intercept
OR
Ax  By  C  0 (general form)
Note: A, B, C are integers or surds

10. Equation of Lines
(Linear Function)
All straight lines can be written in the form;
y  mx  b
m  slope
b  y intercept
OR
Ax  By  C  0 (general form)
Note: A, B, C are integers or surds
e.g. Find the equation of the line perpendicular to y = 5x – 2 , passing
through (0,6) in general form.

11. Equation of Lines
(Linear Function)
All straight lines can be written in the form;
y  mx  b
m  slope
b  y intercept
OR
Ax  By  C  0 (general form)
Note: A, B, C are integers or surds
e.g. Find the equation of the line perpendicular to y = 5x – 2 , passing
through (0,6) in general form.
1
required m  
5

12. Equation of Lines
(Linear Function)
All straight lines can be written in the form;
y  mx  b
m  slope
b  y intercept
OR
Ax  By  C  0 (general form)
Note: A, B, C are integers or surds
e.g. Find the equation of the line perpendicular to y = 5x – 2 , passing
through (0,6) in general form. 1
y   x6
1 5
required m  
5

13. Equation of Lines
(Linear Function)
All straight lines can be written in the form;
y  mx  b
m  slope
b  y intercept
OR
Ax  By  C  0 (general form)
Note: A, B, C are integers or surds
e.g. Find the equation of the line perpendicular to y = 5x – 2 , passing
through (0,6) in general form. 1
y   x6
1 5
required m   5 y   x  30
5

14. Equation of Lines
(Linear Function)
All straight lines can be written in the form;
y  mx  b
m  slope
b  y intercept
OR
Ax  By  C  0 (general form)
Note: A, B, C are integers or surds
e.g. Find the equation of the line perpendicular to y = 5x – 2 , passing
through (0,6) in general form. 1
y   x6
1 5
required m   5 y   x  30
5
x  5 y  30  0

15. Note: lines parallel to the x axis (y = c)

16. Note: lines parallel to the x axis (y = c)
y
x

17. Note: lines parallel to the x axis (y = c)
y
 3, 2 
x

18. Note: lines parallel to the x axis (y = c)
y
 3, 2 
x
y2

19. Note: lines parallel to the x axis (y = c)
y
 3, 2 
x
y2
lines parallel to the y axis (x = k)

20. Note: lines parallel to the x axis (y = c)
y
 3, 2 
x
y2
lines parallel to the y axis (x = k)
y
x

21. Note: lines parallel to the x axis (y = c)
y
 3, 2 
x
y2
lines parallel to the y axis (x = k)
y
 3, 2 
x

22. Note: lines parallel to the x axis (y = c)
y
 3, 2 
x
y2
lines parallel to the y axis (x = k)
y
 3, 2 
x
x3

23. Note: lines parallel to the x axis (y = c)
y
 3, 2 
x
y2
Exercise 5C; 1b, 3cf, 4a,
5d, 6df, 8df, 10b,
11c, 12
lines parallel to the y axis (x = k)
y
 3, 2 
x
x3