1. Don’t let the monster starve bring in any old maths books Fun sums Yum

2. Equation of a Straight Line For any line!

3. What is to be learned? How to find equation of straight line given any two points

4. A (0, 7 )B (2, 11)Equation? m = 11–7 / 2–0 = 4 / 2 = 2 y = 2x + 7 (using y = mx +c ) A (1, 7 )B (2, 11)Equation? m = 11–7 / 2–1 = 4 / 1 = 4 y = 4x + ? 

5. (x,y) (a,b) m = y – b x – a m(x – a) = y – b y – b = m(x – a)

6. Equation in Action Line has gradient 5 and contains point (-4, 3) m = 5(a, b) = (-4, 3) y – b = m(x – a) y – 3 = 5(x + 4) y – 3 = 5x + 20 y = 5x + 20 + 3 y = 5x + 23

7. Equation of any Straight Line use y – b = m(x – a) where m → gradient (a, b) → any point on line Ex 1Line has gradient 4 and contains point (2, 6) m = 4(a, b) = (2, 6) y – 6 = 4(x – 2) y – 6 = 4x – 8 y = 4x – 2

8. Ex 2Line contains points (3, -4) and (6, -2). Equation? Need gradient and point! m = -2 – (-4) 6 – 3 using m = 2 / 3 and (a, b) = (3, -4) y – (-4) = 2 / 3 (x – 3) X3→ 3y + 12 = 2(x – 3) 3y + 12 = 2x – 6 3y = 2x – 18 = 2 / 3

9. Key Question Find the equation of the line connecting A (2, 6) and B (5, 8) m = 8 – 6 y – b = m(x – a) with m = 2 / 3, (a, b) = (2, 6) y – 6 = 2 / 3 (x – 2) 3y – 18 = 2(x – 2) 3y – 18 = 2x – 4 3y = 2x + 14 5 – 2 = 2 / 3

10. Key Question Find the equation of the line connecting A (2, 6) and B (5, 8) m = 8 – 6 y – b = m(x – a) with m = 2 / 3, (a, b) = (5, 8) y – 8 = 2 / 3 (x – 5) 3y – 24 = 2(x – 5) 3y – 24 = 2x – 10 3y = 2x + 14 5 – 2 = 2 / 3

11. Key Question 2 C is the mid point of AB and CD is perpendicular to AB Find the equation of CD. m AB = 10 – 5 m CD = - 3 / 5 (m 1 m 2 = -1) C = (3½, 7½) (mid pt) m = - 3 / 5, (a, b) = (3½, 7½) y – b = m(x – a) y – 7½ = - 3 / 5 (x – 3½) 5y – 37½ = -3(x – 3½) 5y – 37½ = -3x + 10½ 5y = -3x + 48 5 – 2 = 5 / 3 A (2, 5) B(5, 10) D C (3½, 7½) m = - 3 / 5