Final answer:
The common difference in a sequence is similar to the slope in algebra; both describe the rate of change from one point to the next. Specifically, in a linear equation, the slope indicates how much the y-value changes for each unit change in the x-value. The concept is illustrated using a line graph with a slope of 3.
Step-by-step explanation:
The common difference in a mathematical sequence is analogous to the slope in algebra when considering linear functions. For a sequence, the common difference is the amount that each term increases by from one term to the next. In the context of algebra, particularly in the slope-intercept form of a linear equation, which can be written as y = mx + b or y = a + bx, the slope (represented by m or b) is defined as the ratio of the difference in y-values (the rise) to the difference in x-values (the run) between any two points on the line.
According to the provided information in FIGURE A1, the line graph has a slope of 3, which means for every increase of 1 unit on the x-axis (the run), there is an increase of 3 units on the y-axis (the rise). This is consistent along the entire length of the straight line. Hence, for this specific line, the common difference of consecutive y-values for each unit increase in x-value is 3, mirroring the concept of slope in algebra.