A linear function changes at a constant rate. With two table rows, find its slope by dividing the change in output by the matching change in input. Then use that rate to move from a known row to the requested input. Desmos can calculate both expressions. Don't treat the entire output change between the rows as the change for one input unit.
Hints
- Hint 1
The slope tells you how much the output changes when increases by . Subtract the two outputs, then divide by the difference between their inputs. Keep the subtraction order the same in both places.
- Hint 2
A linear function keeps that rate beyond the table. Start at the row where , then count how many input units it takes to reach . How much does the output increase over those units?
Step-by-step
Use the table's rate of change
Step 1Find the change for one input unit
The table pairs with , and with . For a linear function, the slope is the output change divided by the matching input change. Type in Desmos; it prints . So each increase of in adds to the output. Using alone would ignore how far moved.
- Step 2
Move from the known output to
means the output when the input is . Start at : moving from to adds input units, with added to the output for each one. Type on the next Desmos line; it prints . So . Choice A.