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2. Examine the rise in gasoline prices from 1997 to 2006. The price of regular unleaded gasoline in January 1997 was $1.26, and in January 2006, the price of regular unleaded gasoline was $2.31 (“Consumer price index,” 2006). Use the coordinates (1997, 1.26) and (2006, 2.31) to find the slope, or rate of change, between the two points. Describe how you arrived at your answer.
3. The linear equation
represents an estimate of the average cost of gas for year x starting in 1997 (“Consumer price index,” 2006). The year 1997 would be represented by x = 1, for example, because it is the first year in the study. Similarly, 2005 would be year 9, or x = 9.
a. What year would be represented by x = 4?
b. What x-value represents the year 2018?
c. What is the slope, or rate of change, of this equation?
d. What is the y-intercept?
e. What does the y-intercept represent?
f. Assuming this growth trend continues, what will the price of gasoline be in the year 2018? How did you arrive at your answer?
4. The line
represents an estimate of the average cost of gasoline each year. The line
estimates the price of gasoline in January of each year (“Consumer price index,” 2006).
a. Do you expect the lines to be intersecting, parallel, or perpendicular? Explain your reasoning.
b. Use the equations of the lines to determine if they are parallel. What did you find?
c. Did your answer to Part b. confirm your expectation in Part a?
2. A(1997 , 1.26) , B(2006 , 2.31).
Slope = (2.31 - 1.26) / (2006 - 1997) =
1.05 / 9 = 1 1/20 / 9 = (21 /20) / 9 =
21/20 * 1/9 = 7/60.
a. X = 4, 4 = (Y - 1997) + 1
Solve for Y:
4 = Y - 1997 + 1, Y = 2000
b. X = (2018 - 1997) + 1 = 22
Rodney is given two linear equations: x – y = 11 and 2x + y = 19. What value of x should he get as a solution for this system of linear equations?