Theory question 102
Coordinate Geometry(a) Find the equation of the line which passes through the points A(−2, 7) and B(2, −3).
(b) Given that (5b − a)/(8b + 3a) = 1/5, find, correct to two decimal places, the value of a/b.
Show the model answer
Model answer
(a) Gradient = (−3 − 7)/(2 − (−2)) = −10/4 = −5/2
y − 7 = −5/2(x + 2) → 2y − 14 = −5x − 10
5x + 2y − 4 = 0
(b) Cross-multiply: 5(5b − a) = 8b + 3a → 25b − 5a = 8b + 3a
17b = 8a, so a/b = 17/8 = 2.125 ≈ 2.13
Explanation
For (b), collect the a terms on one side and the b terms on the other, then divide.