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?
2. To find the slope, or rate of change, between the two points (1997, 1.26) and (2006, 2.31), you can use the formula for slope:
slope = (change in y) / (change in x)
In this case, the change in y is the difference between the y-coordinates of the two points: 2.31 - 1.26 = 1.05. The change in x is the difference between the x-coordinates: 2006 - 1997 = 9.
So, the slope is 1.05/9 = 0.1167. This means that for every increase of 1 year, the price of gasoline increases by approximately $0.1167.
3. a. The year represented by x = 4 can be found by adding 4 to 1997: 1997 + 4 = 2001. So, x = 4 represents the year 2001.
b. To find the x-value that represents the year 2018, subtract 1997 from 2018: 2018 - 1997 = 21. So, x = 21 represents the year 2018.
c. To find the slope, or rate of change, of the equation, look at the coefficient of the x-term. In this case, the coefficient is 0.05. So, the slope is 0.05, which means that for every increase of 1 year, the average cost of gas increases by $0.05.
d. The y-intercept is the value of y when x = 0. In this equation, the y-intercept is 1.26, which represents the average cost of gas in January 1997.
e. The y-intercept represents the starting point or baseline value of the average cost of gas before any increase or decrease due to time.
f. To estimate the price of gasoline in the year 2018, you can substitute the x-value of 21 into the equation and solve for y:
average cost of gas = 0.05x + 1.26
average cost of gas = 0.05(21) + 1.26
average cost of gas = 1.05 + 1.26
average cost of gas = 2.31
So, the estimated average cost of gas in the year 2018 is $2.31.
4. a. Based on the given information, the lines representing the average cost of gasoline each year and the estimated price of gasoline in January of each year are expected to intersect. This is because the average cost of gasoline each year is a general trend, while the estimated price of gasoline in January represents a specific point in time.
b. To determine if the lines are parallel, we need to compare their slopes. The slope of the first line is 0.05, and the slope of the second line is -0.04. Since the slopes are not equal, the lines are not parallel.
c. No, the answer to Part b does not confirm the expectation in Part a. Instead of being parallel, the lines are expected to intersect, but they can still have different slopes.