the relationship between celsius temperature, c, and fahrenheit temperature, f, can be described by a linear…

the relationship between celsius temperature, c, and fahrenheit temperature, f, can be described by a linear equation in the form f = mc + b. the graph of this equation contains the point (0, 32): water freezes at 0°c or 32°f. the line also contains the point (100, 212): water boils at 100°c or 212°f. write the linear equation expressing fahrenheit temperature in terms of celsius temperature.\nf = □

the relationship between celsius temperature, c, and fahrenheit temperature, f, can be described by a linear equation in the form f = mc + b. the graph of this equation contains the point (0, 32): water freezes at 0°c or 32°f. the line also contains the point (100, 212): water boils at 100°c or 212°f. write the linear equation expressing fahrenheit temperature in terms of celsius temperature.\nf = □

Answer

Explanation:

Step1: Find the slope m

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(0,32)$ and $(x_2,y_2)=(100,212)$. So $m=\frac{212 - 32}{100-0}=\frac{180}{100}=\frac{9}{5}$.

Step2: Find the y - intercept b

The equation of a line is $F = mC + b$. Substituting the point $(0,32)$ (where $C = 0$ and $F=32$) into the equation, we get $32=m\times0 + b$, so $b = 32$.

Step3: Write the linear equation

Substitute $m=\frac{9}{5}$ and $b = 32$ into $F=mC + b$. The equation is $F=\frac{9}{5}C+32$.

Answer:

$F=\frac{9}{5}C + 32$