Question

Given at 68°F equals 20°C and 212°F equals 100°C, develop a linear model for degrees in terms of parentheses F and parentheses and in terms of Celsius parentheses C parentheses. Use your model to convert 10°C into Fahrenheit use your model to find the numeric value in Celsius that is the same in Fahrenheit given the absolute zero, the lowest Possible temperature is -273 Celsius calculate a reasonable domain and range for your model

Answer 1

Step-by-step explanation:

a) From the information given,

68 F = 20 C

212 F = 100C

Let F be the dependent variable and C be the independent variable. F would be on the y axis of the graph while C would be on the x axis. Recall, the equation of a line in the slope intercept form is expressed as

y = mx + b

where

m represents slope

b represents y intercept

The formula for calculating slope is expressed as

m = (y2 - y1)/(x2 - x1)

Considering the given values,

y1 = 68, x1 = 20

y2 = 212, x2 = 100

Thus,

m = (212 - 68) /(100 - 20)= 144/80

m = 1.8

We would find the y intercept, b by substituting m = 1.8, x = 20 and y = 68 into the slope intercept equation. We have

68 = 1.8 * 20 + b

68 = 36 + b

b = 68 - 36

b = 32

The linear model would be

y = 1.8x + 32

Replacing y with F and x with C, the linear model becomes

F = 1.8C + 32

b) The gradient is 1.8. It means that the rate of change of C with respect to F is 1.8.

c) The F intercept is the value of F when C is zero. Thus,

F = 1.8 * 0 + 32

F = 32

F intercept = 32

The F intercept is the temperature in degrees fahrenheit equal to 0 degrees celsius.

d) The C intercept is the value of C when F is zero. Thus,

0 = 1.8C + 32

1.8C = 0 - 32 = - 32

C = - 32/1.8 = - 17.78

C intercept = - 17.78

e) To convert 10 degrees to F, we would substitute C = 10 into the linear model. We have

F = 1.8 * 10 + 32

F = 18 + 32

F = 50

10 degrees celsius = 50 degrees fahrenheit