Exam 3: Thinking Linearly

The cost, in dollars, of filling your gas tank is directly proportional to the price per gallon of gas. If 8 gallons of gas costs $10.00, how much would 11 gallons cost?

Plot each of the following points on the same set of axes.

Graph the line by making a table of ordered pairs and plotting the points. y = 5x - 10

Solve the system using the substitution method.

Plot each of the following points on the same set of axes.

The following table shows the cost of renting a full-size rental car, based on the number of miles driven. a. Explain why a linear equation is appropriate for this relationship. b. Find the slope of the line and explain what it means. c. Find the y-intercept and explain what it means. d. Determine the equation of the line. e. Is this a direct variation relationship? Why or why not? Be specific. f. I am trying to decide whether I can afford to rent a full-size car to drive to St. Louis, which is about 180 miles away. How much would that cost for a one-way trip? How much would it cost for a round trip of 360 miles? g. Why doesn't the round trip cost twice as much as the one-way trip? Be specific.

Mountain climbers use a general rule of thumb which estimates that the temperature will drop 3.5 degrees Fahrenheit for every 1000 ft of elevation. b. Find the slope of the line and explain what it means. c. Find the y-intercept and explain what it means. d. Write the equation of the line. e. Restate your equation in the form of a sentence: "If x represents …, then y = … represents …" f. Use your equation to find the temperature at 10,000 ft.

The table displays the number of women in the US House of Representatives for selected years from 1980 through 2008. a. Use your calculator to determine the line of best fit for these data, where x is the number of years since 1980. Round all coefficients to 4 decimal places. b. What is the correlation coefficient, r? What does it mean about whether this line is a good fit for these data? Explain. c. Give the slope of the line and explain what it means. d. Use this equation to predict the number of women in the House of Representatives in the year 2013.

Graph the line by making a table of ordered pairs and plotting the points.

The following table reports the number of yellow fever cases reported in Ghana for the years 1992-2004 (after the start of mass immunization). b. What trends do you see? Be specific.

Solve the system using the substitution method.

Find the slope of the line that passes through the points (-8, 2)and (-12, 2).

Find the slope and y-intercept.

Which of the following graphs shows the correct location of the point (-3, 4)?

Write an equation of the line with slope and y -intercept

B varies directly as m and inversely n . B=36 when m=54 and n=9 , find B when m= 7 and n=5 .

Graph the line by making a table of ordered pairs and plotting the points. -27y = 14x

Graph the line through the point (-1, 3) having slope -2.

Complete the table of points for the equation y = x - 7.

L varies jointly as a and the square root of b . If L=160 when a=5 and b=16 , find L when and b=144 .