Exam 1: Straight Lines and Linear Functions

Find the point of intersection of the pair of straight lines. y = - 6x - 8 - y = 7x + 14

The size of the average farm in the United States has been growing steadily over the years. The accompanying data, obtained from the U.S. Department of Agriculture, gives the size of the average farm y (in acres) from 1940 through 1997. (Here, x = 0 corresponds to the beginning of the year 1940.) Find the equation of the least-squares line for these data. Use the equation found to estimate the size of the average farm in the year 1982.

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

The relationship between temperature measured in the Celsius scale and the Fahrenheit scale is linear. The freezing point is and , and the boiling point is and , respectively. Find F as a function of C and use this formula to determine the temperature in Fahrenheit corresponding to temperature of .

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. 2x + 2p - 56 = 0 and 5x - 4p + 40 = 0 equilibrium quantity __________ units equilibrium price $ __________

A country is not building many nuclear plants, but the ones it has are running at nearly full capacity. The output (as a percent of total capacity) of nuclear plants is described by the equation where t is measured in years, with corresponding to the beginning of 1990. If the utilization of nuclear power continues to grow at the same rate and the total capacity of nuclear plants in the country remains constant, by what year can the plants be expected to be generating at maximum capacity?

Determine whether the points A (- 2, 5), B (1, 11), C (3, 15) lie on a straight line. Answer yes or no.

Sketch a set of coordinate axes and plot the given point. (2.5, -2.5)

Find the break-even point for the firm whose cost function C and revenue function R are given. C(x) = 10x + 1,000; R(x) = 20x For a break-even operation, the firm should manufacture __________ units of its product, resulting in a break-even revenue of $ __________.

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.

Delivery Charges. A furniture store offers free setup and delivery services to all points within a 24-mi radius of its warehouse distribution center. If you live 20 mi east and 12 mi south of the warehouse, will you incur a delivery charge?

The demand equation for a certain brand of GPS Navigator is x + 5p - 425 = 0, where x is the quantity demanded per week and p is the wholesale unit price in dollars. The supply equation is x - 17p + 1,005 = 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.

Draw a scatter diagram for the data and graph the least-squares line.

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.

The accompanying data were compiled by the superintendent of schools in a large metropolitan area. The table shows the average SAT verbal scores of high school seniors during the 5 years since the district implemented its "back-to-basics" program. Determine the equation of the least-squares line for these data.

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.

Entomologists have discovered that a linear relationship exists between the number of chirps of crickets of a certain species and the air temperature. When the temperature is , the crickets chirp at the rate of , and when the temperature is , they chirp at the rate of . Find N as a function of T and use this formula to determine the rate at which the crickets chirp when the temperature is .

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 positive. c.The slope of the line is negative, and its x-intercept is positive. -

Find the slope of the line shown in the figure.

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b . X = 4y - 8