PLEASE HELP WITH THIS QUESTION ASAP

Question

Doctors have found that a patient’s body temperature can affect their heart rate. The resting heart rate for a patient with a body temperature of 37.1 degrees Celsius, is 65 beats per minute. For each 1-degree increase in body temperature, the heart rate increases by 12 beats per minute.

a. Find an equation for a patient’s resting heart rate in terms of body temperature.

b. What is the estimated body temperature of a patient whose heart rate is 100 beats per minute?

Answer 1

We can start by putting the information into a chart like this:

We can model this using a linear equation since the rate of change is constant.

y = mx+b

m = slope = (change in y)/(change in x) = 12/1 =12

So far we have:

y=12x+b

To find b, we can plug in the point (37.1, 65):

65 = 12(37.1) +b

65= 445.2 + b

b = -380.2

The answer to part A is:

y = 12x -380.2  

For part B, plug in y=100:

100 = 12x-380.2

480.2 = 12x

x = 480.2/12 = 40.0

The answer to part B is:

40 Degrees Celsius

Answer 2

Essentially you are asked to find a linear equation with slope 1 which passes through the point (37.1,65).

That equation is 1=(y-65)/(x-37.1) which can be "massaged" around into a simpler form.

Then use that equation to solve part 2.