Exercise 10 Page 26

Practice makes perfect

a We are told that there is a linear relationship between degrees Celsius and degrees Fahrenheit. We also know two points of this relationship — (0,32) and (100,212). We can draw a straight line through them in the coordinate plane representing the relationship.

To determine the function rule, we use the Slope Formula and the y-intercept, b=32, from the graph.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 0,32) & ( 100,212)

m=212- 32/100- 0

SubTerms

Subtract terms

m=180/100

CalcQuot

Calculate quotient

m=1.8

Let's substitute m=1.8 and b=32 into the slope-intercept form. F=1.8C+32 Here F represents degrees Fahrenheit and C represents degrees Celsius.

b In order to calculate 22° C in terms of degrees Fahrenheit, we use the equation from Part A.

F=1.8C+32 Let's substitute 22 for C.

F=1.8C+32

Substitute

C= 22

F=1.8( 22)+32

Multiply

F=39.6+32

AddTerms

Add terms

F=71.6

Therefore, 22° C is equal to 71.6° F.

c To get an equation that represents degrees Celsius in terms of degrees Fahrenheit, we transform the equation from Part A so that the variable C will end up isolated on one side of the equality.

F=1.8C+32

SubEqn

LHS-32=RHS-32

F-32=1.8C

WriteAsFrac

Write as a fraction

F-32=9/5C

Mult

Multiply by 5/9

C=5/9(F-32)

Thus, C= 59(F-32) is the equation representing degrees Celsius in terms of degrees Fahrenheit.

d In order to calculate 83° F in terms of degrees Celsius, we use the equation we found in Part C.