Question

when the celsius temperature is 30°, the corresponding fahrenheit temperature is 86°. when the celsius temperature is 90°, the corresponding fahrenheit temperature is 194°. let c represent the celsius temperature and f the fahrenheit temperature. a. express f as an exact linear function of c. b. solve the equation in part a for c, thus expressing c as a function of f. c. for what temperature is f = c? a. express f as an exact linear function of c. f = (simplify your answer. do not include the degree symbol in your answer.)

Explanation:

Step1: Find the slope (m) of the linear function

The linear function is in the form \( F = mC + b \). We have two points \((C_1, F_1)=(30, 86)\) and \((C_2, F_2)=(90, 194)\). The slope \( m=\frac{F_2 - F_1}{C_2 - C_1}=\frac{194 - 86}{90 - 30}=\frac{108}{60}=\frac{9}{5} \)

Step2: Find the y - intercept (b)

Substitute \( m = \frac{9}{5} \), \( C = 30 \) and \( F = 86 \) into \( F=mC + b \). So \( 86=\frac{9}{5}\times30 + b \). Calculate \( \frac{9}{5}\times30=54 \). Then \( 86 = 54 + b \), so \( b=86 - 54 = 32 \)

Step3: Write the linear function

Since \( m=\frac{9}{5} \) and \( b = 32 \), the linear function is \( F=\frac{9}{5}C+32 \)

Answer:

\(\frac{9}{5}C + 32\)