Exam 1: Straight Lines and Linear Functions

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 .

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.

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 break-even point for the firm whose cost function C and revenue function R are given. C(x) = 16x + 24,000; R(x) = 24x

Minimizing Shipping Costs. Towns A, B, C, and D are located as shown in the figure. Two highways link town A to town D. Route 1 runs from town A to town D via town B, and Route 2 runs from town A to town D via town C. Suppose a fleet of 100 automobiles are to be shipped from an assembly plant in town A to town D. They may be shipped either by freight train along Route 1 at a cost of 20¢/mile/automobile or by truck along Route 2 at a cost of 18¢/mile/automobile. Which means of transportation minimizes the shipping cost?

The Census Bureau projections of male life expectancy at age 65 in the United States are summarized in the following table. (Here, x = 0 corresponds to the beginning of 2000.) Find the equation of the least-squares line for these data. Use the equation found to estimate the life expectancy at 65 of a male in 2030.

If the line passing through the points and is parallel to the line passing through the points and , what is the value of a? __________

If the line passing through the points (4, a) and (6, - 1) is parallel to the line passing through the points (-3, 1) and (- 1, a + 6), what is the value of a?

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 admissions office at a certain college during the past 5 years. The data relate the number of college brochures and follow-up letters sent to a preselected list of high school juniors who had taken the PSAT and the number of completed applications received from these students (both measured in units of a thousand). Use the least-squares line to predict the number of completed applications expected if 4,400 brochures and follow-up letters are sent out during the next year.

A product may be made using machine I or machine II. The manufacturer estimates that the monthly fixed costs of using machine I are $18,000, whereas the monthly fixed costs of using machine II are $15,000. The variable costs of manufacturing 1 unit of the product using machine I and machine II are $10 and $20, respectively. The products sell for $50 each. What is the maximum profit if the projected sales are 650 units?

Which point has coordinates ( 3, 3)?

Let and be two nonvertical straight lines in the plane with equations and , respectively. Find conditions on , , , and so that and intersect at one and only one point. ​

A division of a corporation manufactures bicycle pumps. Each pump sells for $9, and the variable cost of producing each unit is 40% of the selling price. The monthly fixed costs incurred by the division are $50,000. What is the break-even point for the division?

Determine whether the lines through the given pairs of points are parallel. A (1, - 3), B (- 1, - 5) and C (2, 2), D (- 2, 6)

What are the coordinates of point A?

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

Find the point of intersection of the pair of straight lines. y = - 4x - 9 - y = 5x + 16

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

Find the distance between the given points. (1, 1) and (5, 4)