1. General Form of
Equation of a Straight Line

2. General Form of Equation of a Straight Line
Two unknowns x, y
Ax + By + C = 0
A, B and C are constants.
A and B are NOT both zero.

3. Follow-up question Rewrite the equation of the straight line
L: 2y = -4x + 3 into the general form.
2y = -4x + 3
4x + 2y - 3 = 0
 General form:
Ax + By + C = 0
C = -3
B = 2
A = 4

4. For a straight line L in the general form Ax + By + C = 0, we have:
Substitute y = 0. C By Ax = + C B Ax = +
(0) C Ax By - = C Ax - = A C C y = - x - x = - B B A
Therefore, A C C
slope = - , y -
intercept = -
and x -
intercept = - B B A

5. Follow-up question
Find the slope, the y-intercept and the x-intercept of the straight line 2x + y - 4 = 0.
From the equation, A = 2, B = 1 and C = -4. B A - = 1 2 - =
 Slope 2 - = B C - = ç è æ - = 1 4
y-intercept  4 = A C - = ç è æ - = 2 4
x-intercept  2 =

6. Special Straight Lines
Equations of
Special Straight Lines

7. Oblique Lines Passing Through the Origin
Case 1: Given the slope m
By the slope-intercept form,
y = mx + 0
 y-intercept = 0
The equation of the straight
line L is:
y = mx

8. Case 2: Given the point (a, b)
Slope of L - = a b a b =
The equation of the straight line L is: x a b y =

9. Follow-up question
Find the equation of the straight line passing through the origin and (2, 6).
Slope - = 2 6 3 =
The equation of the straight line is
y = 3x + 0
 y = mx + 0
∴ y = 3x
y-intercept

10. Horizontal Lines
All the points lying on a horizontal line have the same
(-2, ) b
(-1, ) b
(1, ) b
(2, ) b
y-coordinate
The equation of the horizontal line shown is:
y = b

11. Vertical Lines All the points lying on a vertical line have the same .
( , 2) a
( , 1) a
x-coordinate
( , -1) a
( , 2) a
The equation of the vertical line shown is:
x = a