To find the constants $m$ and $b$ for the equation $X = mF + b$, where $F$ is the temperature in degrees Fahrenheit and $X$ is the temperature in the Ava Abate-universal-scale, we can use the two given conditions:

1. When $F = 0$, $X = 21$.
2. When $F = 100$, $X = 112$.

These two points will allow us to determine the slope $m$ and the intercept $b$.

Step 1: Find the slope $m$

The slope $m$ for a straight line is given by the formula: $m = \frac{X_2 - X_1}{F_2 - F_1}$ where:

• $X_1 = 21$ when $F_1 = 0$,
• $X_2 = 112$ when $F_2 = 100$.

Substitute the values: $m = \frac{112 - 21}{100 - 0} = \frac{91}{100} = 0.91$

Step 2: Find the intercept $b$

To find $b$, substitute the value of $m$ and one of the points (either $(0, 21)$ or $(100, 112)$) into the equation $X = mF + b$.

Using the point $(0, 21)$: $21 = 0.91(0) + b$ $b = 21$

Final Formula

Thus, the formula for the Ava Abate-universal-scale is: $X = 0.91F + 21$

Summary:

• $m = 0.91$
• $b = 21$

Would you like further clarification on any part of this? Here are 5 related questions to explore further:

1. How can we use this formula to convert any temperature from Fahrenheit to the new Ava Abate-universal-scale?
2. What would the freezing point of water (32°F) be on the Ava Abate-universal-scale?
3. How would the boiling point of water (212°F) translate to the new scale?
4. Can we express Fahrenheit in terms of $X$ on the Ava Abate-universal-scale?
5. How does this compare to other temperature scales like Celsius or Kelvin?

Tip: When creating any linear relationship, finding the slope is essential, as it defines how two variables change relative to one another.