Chapter 3 . Find a general linear equation (Aa:+By+C = 0, with A, B, C integers)

of the straight line which passes through (5, 2) and (6, —8), and sketch

the line. (4 marks) . Find the slope, y-intercept, and sis—intercept of the line given by

a — 9 = 5y + 3

and sketch its graph. (4 marks) . An oil producer will place 1.5 million barrels of oil per week on the

market when the price is $75 per barrel, and 2.5 million barrels of oil

per week when the price is $90 per barrel. (a) Find the supply equation (giving price as a function of quan-

tity), assuming that price p and quantity q are linearly related. (3 marks)

(b) According to this model, how much will this producer supply if

the price of oil goes to $110 per barrel? (2 marks) . Sketch of a graph of the function f (:3) = —3a:2 + 185s + 7. State the

vertex and y-intercept of the graph of the function. (4 marks) . The demand function for an ofﬁce supply company’s line of fuzzy pen-

cils is p = 23 — 2g, where p is the price per box of pencils when q boxes

are demanded (per week) by consumers. Find the level of production

that will maximize the manufacturer’s total revenue, and determine this revenue (assuming all boxes produced are sold). (4 marks)

. Solve the system of equations 3:1: + 53} 2 14 (4 marks)

23: — y = —8

Solve the s stem of e uations $2 _ y = 11 { 5 marks)

' y q a: — 4y 2 11 . The supply and demand equations for a certain product are supply: 1) = (q + 5)2 demand: p = 440 — %q