Connecting the Rule to the Graph

Property The numerical rule connecting two sequences determines the shape of the graphed line. A multiplicative relationship, like $y = a \cdot x$, creates a line of points that passes through the origin $(0, 0)$. An additive relationship, like $y = x + b$, creates a line of points that does not pass through the origin (unless $b=0$).

Examples Multiplicative: If sequence Y is always 3 times sequence X ($y = 3x$), the points $(1, 3), (2, 6), (3, 9)$ form a line that goes through the origin. Additive: If sequence Y is always 5 more than sequence X ($y = x + 5$), the points $(1, 6), (2, 7), (3, 8)$ form a line that does not go through the origin.

Explanation After you graph the ordered pairs from two sequences, the points form a visual pattern. This pattern is a direct result of the rule that connects the corresponding terms. If one sequence is always a multiple of the other, the graphed line will point directly to the origin $(0, 0)$. If a number is always added or subtracted, the line will be shifted and will not pass through the origin.