Simple Linear Mathematical Relationships in Data (IOD 504)

A relationship is linear when equal steps in the input always produce the same change in the output. You find this by scanning a table with evenly spaced input values and checking whether the output goes up, or down, by the same amount each row. Once you confirm that constant step, you have the whole pattern. You don't need slope formulas or y = mx + b. You just need to count how many steps separate the row you have from the row you want, then add or subtract that constant amount the right number of times.

Reading a table this way turns a question that looks like it needs algebra into simple arithmetic. If dose rises 2 units at a time and yield rises 4.0 g each time, then moving from 2 units to 8 units is three steps, so yield rises by 4.0 g three times, 12.0 g total, added to the starting value. That's it. The skill is noticing the equal spacing, confirming the equal jump, and counting steps, whether you're filling in a missing row, extrapolating past the last row, or interpolating between two given rows.

This connects directly to proportional reasoning, which sits right next to it in data interpretation. A constant rate of change only means a straight line. It does not mean the line passes through the origin, and only lines through the origin are truly proportional, where doubling the input doubles the output. Checking whether a table shows a proportional relationship or just a linear one means looking at the starting value, not just the step size.