A linear function changes at a constant rate, so a question about two input positions calls for the difference between their outputs. Write ending output minus starting output, then evaluate it in Desmos. Change compares two outputs; neither output alone is the change. A negative result means a decrease, while “by how many” asks for the positive size.
Hints
- Hint 1
The knob position is the input, and temperature is the output. The starting and ending temperatures come from putting the two knob positions into . Which temperature should you subtract from which?
- Hint 2
A change is the ending output minus the starting output. The difference between the knob positions is measured in millimeters, not degrees Celsius, so it cannot answer the question by itself.
- Hint 3
The slope of means temperature falls as the knob moves farther from closed. If the output difference is negative, its sign tells you the direction; “by how many” asks for its size.
Step-by-step
Subtract the two temperatures in Desmos
Step 1Translate the knob movement into a temperature difference
The knob moves millimeters, but the question asks for a change in temperature. Since means the temperature at position , write ending temperature minus starting temperature:
The is measured in millimeters, so it isn't the answer.
- Step 2
Find the signed temperature change
Type , then in Desmos. It shows . The negative sign fits the slope, : temperature falls as the knob moves farther from closed.
- Step 3
Report how many degrees the temperature changes
The question asks by how many degrees, so use the size of the change rather than its negative sign. Type ; Desmos shows . The reactor temperature decreases by degrees Celsius. Choice C.