Question

15. The temperature C, in degrees, that is equivalent to a temperature of F degrees Fahrenheit is given by graph of this equation shows the temperature in Celsius for the corresponding temperatures in Fahrenheit.

a. Explain how linear equations can be used in temperature conversion.
b. Explain how could you could use the conversion graph to find the normal body temperature in degrees Celsius, which is 98.6°F.

Answer 1

For A: The linear equation is
`C=(5)/(9)F-(32)/(9)`

For B: The temperature of normal body in degree Celsius is 37° C.

Step-by-step explanation:

• For A:

Linear equations are defined as the equations in which the highest power of a variable is '1'. The general equation for a linear equation is:

`y=mx+c`

where,

y = Y-coordinate

m = slope of the line

x = X - coordinate

c = intercept on y-axis

For the given equation:

`C=(5)/(9)(F-32)`

The linear equation representation for the given equation is:

`C=(5)/(9)F-(32)/(9)`

• For B:

We are given a value of temperature in degree Fahrenheit. To calculate its value in degree Celsius, we use the equation above.

Putting value of F = 98.6 in above equation, we get:

`C=((5)/(9)* 98.6)-(32)/(9)\\\\C=37`

Hence, the temperature of normal body in degree Celsius is 37° C.

Answer 2

A. How can the equation be used in temperature conversion?

You take the conversion equation C = (5/9) (F - 32) and you replace the F by the value of Fahrenheit degrees... then solve the calculations to get the degrees in Celsius.

For example, if you have 80°F to convert in °C:

C = (5/9) (80 - 32) = (5/9) (48) = 26.66 °C

B. How can you use the graph to find the body temp in C?

Using the graph will give a very imprecise measure due the scale of the graph.

But you would have to find 98.6 on the axis of X (it represents the °F), then go upwards until you find the line....

Then report that position on the line on the Y-axis (representing the °C) to get your measure.