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.

Question

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.

Answer 1

To find the slope, or rate of change, between the two given points (1997, 1.26) and (2006, 2.31), we can use the formula for slope:

Slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Let's plug in the values into the formula:

Slope = (2.31 - 1.26) / (2006 - 1997)

Slope = 1.05 / 9

Slope ≈ 0.1167

Therefore, the slope, or rate of change, between the two points is approximately 0.1167.

To arrive at this answer, I subtracted the y-coordinate of the first point (1.26) from the y-coordinate of the second point (2.31) to get the change in the y-values. Then, I subtracted the x-coordinate of the first point (1997) from the x-coordinate of the second point (2006) to get the change in the x-values. Finally, I divided the change in y-values by the change in x-values to find the slope.