ACT (Enhanced)MathematicsEasy
A technician is calibrating a sensor that measures temperature. The sensor's reading (R) in ohms is linearly related to the actual temperature (T) in degrees Celsius. If the sensor reads 500 ohms at 0°C and 700 ohms at 100°C, what is the sensor reading at 25°C?
- A600 ohms
- B575 ohms
- C550 ohms
- D525 ohms
Show answer & explanationAnswer & explanation
Correct answer: C. 550 ohms
To find the sensor reading at 25°C, first determine the linear relationship between resistance and temperature. Calculate the slope (rate of change) and then use the point-slope form or y=mx+b to find the equation. Finally, substitute 25 for T to find R.
Why the other options are wrong
- A. This option might result from assuming a constant increment per 10°C, or a miscalculation of the slope.
- B. This option might arise from an arithmetic error in calculating the slope or intercept.
- D. This option results from incorrectly assuming a direct proportionality from 0°C or miscalculating the slope.
Linear Interpolation
Estimating a value within two known values on a linear scale.
- Assumes a constant rate of change.
- Requires at least two data points.
- Used to predict intermediate values.
Memory trick: Slope's path, point's start, equation's heart.