Question

I am not sure how to do these two assignemnts: 1) An oven is turned on and set to reach a desired temperature of 350 degrees Fahrenheit. The oven warms up at a constant rate. The oven’s temperature is 134 degrees Fahrenheit at 1 minute and it reaches its desired temperature at 5 minutes. Write a linear function for the temperature T, in degrees Fahrenheit, of the oven m minutes from the time it was turned on until it reaches the desired temperature. A. T ( m ) = 54 m + 350 T ( m ) = 54 m + 350. 2) What is the equation of the line that passes through the origin and is perpendicular to the line 4x+3y=6

Answer 1

The desired temperature is 350 degrees Fahrenheit at 5 minutes.

The oven's temperature is 134 degrees Fahrenheit at 1 minute.

$(1,134),(5,350)$

Since, it is a linear function, we have;

$\begin{gathered} T(m)=sm+c \\ \text{Where s is the constant rate.} \\ s=\frac{y_2-y_1}{x_2-x_1} \\ s=\frac{350-134}{5-1} \\ s=\frac{216}{4} \\ s=54 \end{gathered}$

Then, applying the point slope formula, we have;

$\begin{gathered} y-y_1=m(x-x_1) \\ y-134=54(x-1) \\ y=54x-54+134 \\ y=54x+80 \end{gathered}$

Relating it back to the context of the question, we have;

$\begin{gathered} T(m)=54m+80 \\ \text{Where T(m)= temperature and m= minutes} \end{gathered}$