©G Dear2008 – Not to be sold/Free to use Stage 4 Year 9 Coordinate Geometry Equation of a Straight Line Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use

We must be able to convert between forms. Equation of a Straight Line Two types of equation. 1. Gradient-Intercept Form y = mx +b Gradient y-Intercept 2. General Form ax +by + c = 0 ‘a’ always positive. ‘b’ NOT y-intercept Always ‘0’ We must be able to convert between forms.

Equation of a Straight Line Write in General Form a) y = 2x + 3 b) 2y = x +7 -y -y -2y -2y 0 = 2x – y + 3 0 = x – 2y +7 2x –y +3 = 0 x – 2y +7 = 0 x 3 x3 c) y = -x + 6 d) y = +3 x3 +x -6 +x -6 x3 x + y - 6 = 0 3y = x + 9 -3y -3y 0 = x -3y + 9 x -3y + 9 = 0

Equation of a Straight Line Write in Gradient-Intercept Form a) 3y = 9x + 6 b) 5y = 2x + 1 ÷3 ÷3 ÷3 ÷5 ÷5 ÷5 y = 3x + 2 2 5 1 5 y = x + c) y - 2x = 0 d) 3y + x -1 = 0 +2x +2x -x +1 -x +1 y = 2x 3y = -x +1 ÷3 ÷3 ÷3 -1 3 1 3 y = x +

Equation of a Straight Line Write the Gradient and Y-Intercept 1 2 a) y = 9x + 6 b) y = x - 1 1 2 m = 9 m = b = 6 b = -1 c) y = 2x d) y = x + 7 m = 2 m = 1 b = 0 b = 7

Equation of a Straight Line Write the equation. y = mx + b 2 3 a) m=2 b=1 b) m= b=-5 y = 2x + 1 2 3 y = x - 5 c) m=-4 b=-1 d) m=12 b=7 y = -4x - 1 y = 12x + 7

Write the equation as y=mx+b and state m and b. Equation of a Straight Line Write the equation as y=mx+b and state m and b. a) y – 2x = 1 b) 2y = 3x + 7 +2x +2x ÷2 ÷2 ÷2 y = 2x + 1 3 2 7 2 y = x + m = 2 3 2 m = b = 1 7 2 b =

Is the point given on the line? Equation of a Straight Line Is the point given on the line? a) y = 2x + 1 (2,5) b) 2y = 3x + 7 (1,4) 5 = 2x2 + 1 2x4 = 3x1 + 7 5 = 5 Yes 8 = 10 No c) y – 2x = 1 (1,3) d) y = 5x + 1 (1,5) 3 - 2x1 = 1 5 = 5x1 + 1 1 = 1 Yes 5 = 6 No