General Form of Equation of a Straight Line

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.

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

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

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 =

Special Straight Lines Equations of Special Straight Lines

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

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 =

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

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

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