Exam 1: Straight Lines and Linear Functions

Which point has coordinates (- 2, 2)?

The demand equation for the Schmidt-3000 fax machine is , where x is the quantity demanded per week and p is the unit price in dollars. The supply equation is , where x is the quantity the supplier will make available in the market when the unit price is p dollars. Find the equilibrium quantity and the equilibrium price for the fax machines.

Will Barclay wishes to determine which antenna he should purchase for his home. The TV store has supplied him with the following information: Will wishes to receive Channel 17 (VHF), which is located 29 miles east and 33 miles north of his home, and Channel 38 (UHF), which is located 25 miles south and 34 miles west of his home. Which model will allow him to receive both channels at the least cost? (Assume that the terrain between Will's home and both broadcasting stations is flat.)

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 lines with equation and , where and , are perpendicular to each other.

Find the constants m and b in the linear function so that and .

Find an equation of the circle that satisfies the given conditions. Center at the origin and passes through (5, 1)

Metro Department Store's annual sales (in millions of dollars) during 5 years were Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.

A division of a corporation manufactures bicycle pumps. Each pump sells for $7, and the variable cost of producing each unit is 60% of the selling price. The monthly fixed costs incurred by the division are $80,000. What is the break-even point for the division? break-even production __________ units break-even revenue $ __________

An office building worth $1 million when completed in 2000 is being depreciated linearly over 80 years. What will be the book value of the building in 2048? (Assume the scrap value is $0.)

Find the slope of the line shown in the figure.

Find the point of intersection of the pair of straight lines. y = 3x + 8 Y = - 3x + 32

The quantity demanded each month of Russo Espresso Makers is 250 when the unit price is $125.00. The quantity demanded each month is 1,100 when the unit price is $91.00. The suppliers will market 700 espresso makers if the unit price is $74.00 or lower. At a unit price of $109.00, they are willing to make available 2,450 units in the market. Both the demand and supply equations are known to be linear. Find the equilibrium quantity and the equilibrium price.

The quantity demanded for a certain brand of portable CD players is 400 units when the unit price is set at $80. The quantity demanded is 1,400 units when the unit price is $30. Find the demand equation.

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

With computer security always a hot-button issue, demand is growing for technology that authenticates and authorizes computer users. The following table gives the authentication software sales (in billions of dollars), including projections, from 1999 through 2004. (Here, x = 0 represents 1999.) Find an equation of the least-squares line for these data. Please round the coefficients in your equation to three decimal places. Use the result to estimate the sales for 2005, assuming the projection is accurate.

The demand equation for a certain brand of fax machine is 5x + p - 2,350 = 0, where x is the quantity demanded per week and p is the unit price in dollars. The supply equation is 4x - 5p + 1,600 = 0, where x is the quantity the supplier will make available in the market when the unit price is p dollars. Find the equilibrium quantity and the equilibrium price for the fax machines. equilibrium quantity __________ units equilibrium price $ __________

Metro Department Store's annual sales (in millions of dollars) during 5 years were Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.

Find the slope of the line shown in the figure.

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.

Sketch a set of coordinate axes and plot the given point. (5, -8)