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What is the pressure in kPa at 21.3 degrees Celsius? Write answer to the hundredths place.

The linear equation from the graph is given as:

\[
y = mx + b
\]
where:

- \( m = 0.29587 \) (slope)
- \( b = 93.687 \) (y-intercept)
- \( x \) represents the temperature (in °C)
- \( y \) represents the pressure (in kPa)

We need to find the pressure \( y \) at a temperature of \( x = 21.3 \) °C. Substituting \( x = 21.3 \) into the equation:

\[
y = 0.29587 \cdot 21.3 + 93.687
\]

Let me calculate that.

\[
y = 0.29587 \cdot 21.3 + 93.687 = 6.301 + 93.687 = 99.99
\]

The pressure at 21.3 °C is **99.99 kPa**.

Would you like more details or have any questions? Here are some related questions:

1. How does the correlation coefficient \( r = 0.99999 \) affect the accuracy of the fit?
2. What does the root mean square error (RMSE) tell us about the linear fit quality?
3. How does temperature generally affect pressure in a system like this?
4. If the slope \( m \) were to change, how would it affect pressure predictions?
5. Can this linear model be used for temperature values beyond the data range shown?

**Tip**: Always check the units when working with real-world equations to ensure correct conversions.

Learn how to calculate the pressure at 21.3°C using the linear equation y = 0.29587x + 93.687. This problem covers key algebraic and physical concepts, including the relationship between temperature and pressure. The solution involves substitution and solving for y, resulting in a pressure of 99.99 kPa.

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