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sologuitar

Member

Registered: 2022-09-19

Posts: 467

Find A Linear Equation

The relationship between Celsius (°C) and Fahrenheit (°F) degrees of measuring temperature is linear. Find a linear equation relating °C and °F if 0°C corresponds to 32°F and 100°C corresponds to 212°F.

Can I get a few hints?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,181

Re: Find A Linear Equation

If C is the across coordinate and F the up coordinate the 32F is the intercept with up axis.

(0,32) and (100, 212) are known points so substitute in y = mx + c ie. F = m.C + c where C is the centigrade and c is the intercept.

You've met this formula in another question for changing the subject of a formula.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Find A Linear Equation

The relationship between Celsius (°C) and Fahrenheit (°F) degrees of measuring temperature is linear. Find a linear equation relating °C and °F if 0°C corresponds to 32°F and 100°C corresponds to 212°F.

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Find A Linear Equation

If C is the across coordinate and F the up coordinate the 32F is the intercept with up axis.

(0,32) and (100, 212) are known points so substitute in y = mx + c ie. F = m.C + c where C is the centigrade and c is the intercept.

You've met this formula in another question for changing the subject of a formula.

Bob

Are you talking about the slope formula or the point-slope formula?

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Find A Linear Equation

The relationship between Celsius (°C) and Fahrenheit (°F) degrees of measuring temperature is linear. Find a linear equation relating °C and °F if 0°C corresponds to 32°F and 100°C corresponds to 212°F.

Which one? There are two formulas here. The slope formula or the point-slope formula or both?

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Find A Linear Equation

The relationship between Celsius (°C) and Fahrenheit (°F) degrees of measuring temperature is linear. Find a linear equation relating °C and °F if 0°C corresponds to 32°F and 100°C corresponds to 212°F.

Which one? There are two formulas here. The slope formula or the point-slope formula or both?

Last edited by amnkb (2023-11-22 12:16:52)

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Find A Linear Equation

The relationship between Celsius (°C) and Fahrenheit (°F) degrees of measuring temperature is linear. Find a linear equation relating °C and °F if 0°C corresponds to 32°F and 100°C corresponds to 212°F.

Which one? There are two formulas here. The slope formula or the point-slope formula or both?

Why can't you simply answer the question?
Why do I need to click to see the answer?
I prefer your reply in LaTex form.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,181

Re: Find A Linear Equation

http://www.mathisfunforum.com/viewtopic … 44#p436044

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 164

Re: Find A Linear Equation

Perhaps you were expecting a solution like this:

The linear formula is of the form:
F = aC + b
where,
F= Fahrenheit (°F) degrees
C= Celsius (°C) degrees
'a' and 'b' are the unknown parameters to be found.

If C=0, F=32, then
32 = a*0 + b
b=32 , the intercept with the F,  up, axis.

if C=100, F=212
212 = a*100 + 32 [was b]
212 - 32 = a*100
180 = a*100
a = 180/100 = 1.8 , the slope of the line (usually called m)

Note:
The slope m (or 'a' here) could be calculated directly if we know two points (x1,y1) and (x2,y2).
Here, x1=C1=0 and y1=F1=32, also x2=C2=100 and y2=F2=212
m= (y2-y1)/(x2-x1) = (F2-F1)/(C2-C1) = (212-32)/(100-0) = 180/100 = 1.8

C=1.8*F + 32

Sorry, I wrote the lines above while I am sure that you know them already.

Last edited by KerimF (2023-11-23 04:23:24)

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Find A Linear Equation

Ok. You know your math. Terrific!