Exam 1: Straight Lines and Linear Functions

Let and be two nonvertical straight lines in the plane with equations and , respectively. Find conditions on , , and so that and intersect at infinitely many points.

Determine whether the lines through the pair of points are parallel. and

Find an equation of the line passing through the origin and parallel to the line passing through the points (1, 5) and (3, 9).

A division of a corporation produces "Personal Income Tax" diaries. Each diary sells for $4. The monthly fixed costs incurred by the division are $6,000, and the variable cost of producing each diary is $2. Find the break-even point for the division. break-even production __________ units; break-even revenue $ __________. What should be the level of sales in order for the division to realize a 15% profit over the cost of making the diaries? __________ units

The quantity demanded each month of Russo Espresso Makers is 200 when the unit price is $120.00. The quantity demanded each month is 1,000 when the unit price is $80.00. The suppliers will market 850 espresso makers if the unit price is $42.00 or lower. At a unit price of $72.00, they are willing to make available 2,350 units in the market. Both the demand and supply equations are known to be linear. Find the equilibrium quantity and the equilibrium price.

Find the equation of the least-squares line for the given data. Draw a scatter diagram for the given data and graph the least-squares line.

Refer to the accompanying figure and determine the coordinates of the given point and the quadrant in which it is located.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The circle with equation lies inside the circle with equation , provided .

Sketch a set of coordinate axes and plot the given point. (-4, 3)

For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price. 5x + 2p - 69 = 0 and 5x - 4p + 33 = 0

The annual sales of Crimson Drug Store are expected to be given by million dollars t years from now, whereas the annual sales of Cambridge Drug Store are expected to be given by million dollars t yr from now. When will Cambridge's annual sales first surpass Crimson's annual sales? Please round your answer to one decimal place if necessary. __________ yr

College admissions officers estimate that 55% of the students who are offered admission to the freshman class at the university will actually enroll.Find an equation that expresses the relationship between the number of students who actually enroll (y) and the number of students who are offered admission to the university (x).If the desired freshman class size for the upcoming academic year is 1,650 students, how many students should be admitted? Equation: y = __________ Number of students: __________

Find the slope of the line shown in the figure.

Find the break-even point for the firm whose cost function C and revenue function R are given. Round the intermidiate calculations to nearest integer. C(x) = 180x + ; R(x) = 300x

Find the break-even point for the firm whose cost function C and revenue function R are given. ;

Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.

A manufacturer has a monthly fixed cost of $35,000 and production cost of $4 for each unit produced. The product sells for $10/unit. Compute the profit (loss) corresponding to production level of 8,000 units.

Refer to the accompanying figure and determine the coordinates of the given point. ​ ​ Coordinates: __________ ​ Determine the quadrant in which it is located: __________

Minimizing Shipping Costs. Towns A, B, C, and D are located as shown in the figure. Two highways link town A to town D. Route 1 runs from town A to town D via town B, and Route 2 runs from town A to town D via town C. Suppose a fleet of 100 automobiles are to be shipped from an assembly plant in town A to town D. They may be shipped either by freight train along Route 1 at a cost of 20¢/mile/automobile or by truck along Route 2 at a cost of 18¢/mile/automobile. ​ ​ Which means of transportation minimizes the shipping cost? ​ __________ ​ What are the net savings? ​ $__________

Find the distance between the given points. (2, 1) and (6, 4)