Questions: The relationship between the actual air temperature x (in degrees Fahrenheit) and the temperature y adjusted for wind chill (in degrees Fahrenheit, given a 20 mph wind) is given by the following formula: y=-22+1.4x Estimate the actual temperature if the temperature adjusted for wind chill is -15 degrees Fahrenheit.

The relationship between the actual air temperature x (in degrees Fahrenheit) and the temperature y adjusted for wind chill (in degrees Fahrenheit, given a 20 mph wind) is given by the following formula: y=-22+1.4x Estimate the actual temperature if the temperature adjusted for wind chill is -15 degrees Fahrenheit.
Transcript text: The relationship between the actual air temperature $x$ (in degrees Fahrenheit) and the temperature $y$ adjusted for wind chill (in degrees Fahrenheit, given a 20 mph wind) is given by the following formula: \[ y=-22+1.4 x \] Estimate the actual temperature if the temperature adjusted for wind chill is -15 degrees Fahrenheit.
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Solution

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Solution Steps

To estimate the actual temperature given the wind chill temperature, we need to solve the equation for \( x \) when \( y = -15 \). This involves rearranging the formula to isolate \( x \) and then substituting the given value of \( y \).

Step 1: Understand the Given Formula

The relationship between the actual air temperature \( x \) and the temperature adjusted for wind chill \( y \) is given by the formula: \[ y = -22 + 1.4x \]

Step 2: Substitute the Given Value

We are given that the temperature adjusted for wind chill is \( y = -15 \). Substitute this value into the formula: \[ -15 = -22 + 1.4x \]

Step 3: Solve for \( x \)

To find the actual temperature \( x \), rearrange the equation to solve for \( x \): \[ 1.4x = -15 + 22 \] \[ 1.4x = 7 \] \[ x = \frac{7}{1.4} \] \[ x \approx 5.0 \]

Final Answer

\[ \boxed{x = \frac{35}{7} = 5} \]

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