Problem Sheet 2

Problem Sheet – 2 1. Compute the slope of the segment joining each pair of points: (i) (0, 0), (2, 2) (ii) (6, − 1), (−2, 0) (iii) (−3, 5), (4, − 2) (iv) (−3, − 2), ( −3, − 4) (v) (2.5, 7), (7.5, − 3) 2. Which of the following segments is horizontal and which is vertical? (i) The segment joining (4, − 6) and (10, − 6) . (ii) The segment joining (4, − 6) and (4, 10). (iii) The segment joining (0, 6) and (0, − 6) . (iv) The segment joining (4, 0) and (10, 0) . 3. A line segment fitted to points whose coordinates are in the order (Disposable income, Consumption expenditures) for the United States in recent years passes through (32, 30) and (57, 54) , where the numbers are in billions of dollars. What is the slope of the segment and interpret it? From this result, identify of MPC and MPS and interpret of them. 4. Write the general equation of a straight line? If y = 0.8 x + 2 , (a) write the coordinates of the points where x = 0 and x = 5 . (b) Compute the slope from the points used in (a). 5. (a) Write an equation in the slope intercept form. Write (i) 2 y + 3 x = 18 (ii) 3 y − 2 x = 24 in the slope intercept form. (b) What is the slope of the line? (c) What is the x- intercept and y- intercept form? (d) Write the coordinates of the points found in (c) and also draw this line. 6. A publisher asks a printer for quotations on the cost of printing 1,500 and 2,500 copies of a book. The printer quotes $5,500 for 1,500 copies and $8,500 for 2,500 copies. Assume that cost, y is linearly related to x, the number of books printed. a) Write the equation of the given line. b) What is the cost of printing 3,500 copies? 7. A printer quotes the price of Taka 1400 for printing 200 copies of a report and Taka 2900 for printing 500 copies. Assuming a linear relationship, what would be the price for printing 800 copies? 8. An agency rents Cars for one day and charges $22 plus 20 cents per mile the Car is driven. (a) Write the equation for the cost of one day’s rental, y, in terms of x, the number of miles driven. (b) Interpret the slope and the y- intercept. (c) What is the renter’s average cost per mile if a Car is driven 100 miles? 200 miles?

9. Solve the equation 2.25 p + 1.80c = 31.50 for p in terms of c and also for c in terms of p in slope-intercept form (both cases), then find the slope in both cases. 10. Find the equation of the line that passing through the given point and having the given slope: (i) (4, 3) and slope -0.50 (ii) (8, 10) and slope 0.75 (iii) (3, 4) and slope 3 (iv) (−5, − 8) and slope 13. 11. Find the equation of the line passing through each of the given pair of points: (i) (−4, 7) and (−4, − 3) (ii) (4, − 6) and (10, − 6) (iii) (4, 6) and (−3, 7) (iv) (3, 6) and (8, 6) . 12. (a) What is the equation of the line that has a slope of - 5 (minus five) and intercept Y-axis at 10? (b) Find out the equation of the line passing through (6,0) and (0,9). Draw the graph (free hand). 13. (a) What do you know about the total cost, variable cost, fixed cost, Marginal cost and average cost. Interpret the equation y = 3x +2 for the above explanation. (b) Define supply, demand, cost, revenue, profit functions and break-even. 14. A manufacturer of cassette tapes has a fixed cost of $60,000 and a variable cost of $6 per cassette produced. Selling price is $9 per cassette. a) Find the revenue, cost and profit functions. b) What is the profit if 25,000 cassettes are made and sold? c) What is the profit if 18,000 cassettes are made and sold? d) At what number of cassettes made and sold will the manufacturer break-even? e) What is the break-even dollar volume of sales (revenue)? 15. The total cost, y, of producing x units is a linear function. Records show that an one occasion 100 units were made at a total cost of $200, and an another occasion, 150 units were made at a total cost $275. (a) (b)

Write the linear equation for the total cost in terms of the number of units produced. What is the total cost if 250 units are made?

16. Which of the following pairs of lines are parallel and perpendicular? (a) 2 x + 3 y + 6 = 0; 3 x − 2 y + 9 = 0 (b) 4 x + 3 y + 6 = 0; 4 x + 3 y + 17 = 0 The End