Exam 1: Straight Lines and Linear Functions

A certain economy's consumption function is given by the equation where is the personal consumption expenditure in billions of dollars and x is the disposable personal income in billions of dollars. Find , , and .

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

Find an equation of the line that passes through the points. and

The accompanying table gives the forecast for the worldwide sales (in billions of dollars) of information security through 2007 (t = 0 corresponds to 2002): Find an equation of the least-squares line for these data. Use the result to estimate the spending on information security software in 2008, assuming that the trend continued. Round your answers to two decimal places.

The demand equation for a certain brand of GPS Navigator is x + 5p - 950 = 0, where x is the quantity demanded per week and p is the wholesale unit price in dollars. The supply equation is x - 19p + 1,210 = 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 . 6x + 7y = 14

Cowling's rule is a method for calculating pediatric drug dosages. If a denotes the adult dosage (in milligrams) and if t is the child's age (in years), then the child's dosage is given by If the adult dose of a drug is 500 mg, how much should a 4 year-old child receive?

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

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

Determine whether the points A (- 2, 2), B (3, 12), C (1, 8) lie on a straight line.

Which point has coordinates (4, 4)? ​

A manufacturer of 24-hr variable timers, has a monthly fixed cost of $56,000 and a production cost of $9 for each timer manufactured. The units sell for $16 each. Find the break-even point algebraically.

Find the slope of the line that passes through the given pair of points. (- 1, 5) and (7, 8)

Find an equation of the vertical line that passes through .

Find the slope of the line shown in the figure.

Determine whether the lines through the pair of points are parallel. Answer yes or no. and

Find an equation of the horizontal line that passes through (-5, -6) .

Cowling's rule is a method for calculating pediatric drug dosages. If a denotes the adult dosage (in milligrams) and if t is the child's age (in years), then the child's dosage is given by Is D a linear function of ? Hint: Think of as having the form . If the adult dose of a drug is 510 mg, how much should a 4 year-old child receive? Please round the answer to two decimal places. __________ milligrams

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.

According to industry sources, online banking is expected to take off in the near future. The projected number of households (in millions) using this service is given in the following table: (Here, x = 0 corresponds to the beginning of 1998.) 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 number of households using online banking at the beginning of 2007, assuming the projection is accurate.