Exam 1: Straight Lines and Linear Functions

The quantity demanded of a certain brand of DVD player is 3,500/wk when the unit price is $460. For each decrease in unit price of $20 below $460, the quantity demanded increases by 250 units. The suppliers will not market any DVD players if the unit price is $400 or lower. But at a unit price of $445, they are willing to make available 500 units in the market. The supply equation is also known to be linear. Find the equilibrium quantity and the equilibrium price.

Sketch a set of coordinate axes and plot the given point. (-1, 4)

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. p = - 0.3x + 5.9 and p = 0.15x + 0.05 equilibrium quantity __________ units equilibrium price $ __________

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

Match each graph below with the letter of the corresponding slope description. a.The slope of the line is undefined. b.The slope of the line is positive, and its y-intercept is negative. c.The slope of the line is negative, and its x-intercept is negative. -

Which point has a negative x-coordinate and a negative y-coordinate?

Sketch a set of coordinate axes and plot the given point.

Assume that a certain commodity's demand equation has the form p = ax + b, where x is the quantity demanded and p is the unit price in dollars. Suppose the quantity demanded is 3,000 units when the unit price is $17.00 and 7,000 when the unit price is $13.00. What is the quantity demanded when the unit price is $15.50? __________ units

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. Please round the coefficients in your equation to three decimal places.

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.

The demand equation for a certain brand of GPS Navigator is x + 3p - 765 = 0, where x is the quantity demanded per week and p is the wholesale unit price in dollars. The supply equation is x - 18p + 390 = 0, where x is the quantity the supplier will make available in the market when the wholesale price is p dollars each. Find the equilibrium quantity and the equilibrium price for the GPS Navigators. equilibrium quantity __________ units equilibrium price $ __________

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b.

Find an equation of the line that passes through the points (3, 7) and ( -6, -2)

The demand equation for a certain brand of GPS Navigator is x + 3p - 565 = 0, where x is the quantity demanded per week and p is the wholesale unit price in dollars. The supply equation is x - 16p + 480 = 0, where x is the quantity the supplier will make available in the market when the wholesale price is p dollars each. Find the equilibrium quantity and the equilibrium price for the GPS Navigators.

Sketch a set of coordinate axes and plot the given point. (4, 2)

Find the break-even point for the firm whose cost function C and revenue function R are given. C(x) = 12x + 7,000; R(x) = 19x For a break-even operation, the firm should manufacture __________ units of its product, resulting in a break-even revenue of $ __________.

Find an equation of the circle that satisfies the conditions. Center and passes through

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b . If not, answer non-linear. x = 3y - 18

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. p = - 3x + 29 and p = 4x + 1 equilibrium quantity __________ units equilibrium price $ __________

Distance Traveled. A grand tour of four cities begins at city A and makes successive stops at cities B, C, and D before returning to city A. If the cities are located as shown in the figure, find the total distance covered on the tour.