Exam 1: Straight Lines and Linear Functions

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.) $ __________ What will be the book value of the building in 2072? (Assume the scrap value is $0.) $ __________

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 = - 2x + 15 and p = 5x + 1

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.

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 point (1, k) lies on the line with equation 3x + 2y = 6 if and only if .

Find the slope of the line shown in the figure.

The quantity demanded of a certain brand of DVD player is 3,300/wk when the unit price is $455.00. For each decrease in unit price of $5.00 below $455.00, the quantity demanded increases by 100 units. The suppliers will not market any DVD players if the unit price is $350.00 or lower. But at a unit price of $374.00, they are willing to make available 2,400 units in the market. The supply equation is also known to be linear. Find the equilibrium quantity and price.

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

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.

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 .

The accompanying table gives the projected online spending per buyer (in dollars) from 2002 (x = 0) through 2008 (x = 6): Find an equation of the least-squares line for these data. Use the result to estimate the rate of change of spending per buyer between 2002 and 2008. Round your answers to two decimal places.

Which point has coordinates (-5, 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 = - 0.5x + 11.5 and p = 0.25x + 3.25

Which point has coordinates (-2, 2)?

If the line passing through the points (1, a) and (3, - 2) is parallel to the line passing through the points (3, 7) and (- 5, a + 6) , what is the value of a?

Find an equation of the circle that satisfies the given conditions. Radius 2 and center at the origin.

According to the Massachusetts Department of Welfare, the spending (in billions of dollars) by Medicaid, the national health-care plan for the poor, over the 5-yr period from 1988 to 1992 is summarized in the accompanying table. (Here, x = 0 represents the beginning of the year 1988.) 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 of to estimate Medicaid spending for the year 1994, assuming the trend continued.

Find an equation of the circle that satisfies the given conditions. Radius 6 and center (3, - 5)

Match the statement with one of the graphs. ​ The slope of the line is negative, and its x-intercept is negative. ​

Find the point of intersection of the pair of straight lines. 3x - 5y = 5 2x + 15y = 7

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. If the distance between the points and is D, then the distance between the points and is given by kD.