Welcome to a lesson on converting temperature between celsius and fahrenheit.
We'll derive the formulas used to do the conversions,
as well as convert between celsius and fahrenheit.
Since the relationship between
celsius and fahrenheit is linear, we can determine the conversion equation
by determining two key temperatures for both celsius and fahrenheit.
For example, the freezing temperature for celsius is zero degrees,
and the freezing temperature for fahrenheit is thirty-two degrees.
We could represent this information as a point,
or an ordered pair. This would be the point, zero, thirty-two.
And the boiling temperature for celsius is one hundred degrees
and the boiling temperature for fahrenheit is two hundred twelve degrees.
And we could represent this information as an ordered pair.
The second part would be one hundred, comma,
two hundred twelve.
So now that we have two points on the line that relates
celsius and fahrenheit, we could determine the equation of the line,
by determining the slope of the line,
and the y-intercept of the line.
So to visualize what we've just done, we're going to use the point, zero, thirty-two,
and the point, one hundred, two hundred twelve
to determine the equation of this line,
which we could use to convert between celsius and fahrenheit.
So the first step to determine the equation of our line
is going to be to determine the slope given these two points.
So we'll go ahead and call this x sub-one, y sub-one,
x sub-two, y sub-two.
So our slope is going to be equal to
two hundred twelve minus thirty-two divided by
one hundred minus zero.
So we'll have one hundred eighty all over one hundred.
The greatest common factor of these two would be twenty,
so the slope of the line would be nine-fifths.
Normally when determining the equation of the line,
we also have to determine the y-intercept, which would be b.
But in this case, we have the point, zero, thirty-two,
so thirty-two would be the y-intercept.
So the equation of the line is y equals nine-fifths x, plus thirty-two.
But x actually represents the temperature in celsius,
and y represents the temperature in fahrenheit.
So we'll go ahead and write this is terms of f and c.
So we'll have f equals nine-fifths times c, plus thirty-two.
So we'll use this equation to convert celsius to fahrenheit.
And then to convert fahrenheit to celsius, we can just take this equation and solve for c.
We could use this equation in it's current form,
but it will be helpful to solve it for c.
So if we have f equals nine-fifths times c, plus thirty-two.
if we want to solve for c, we should subtract thirty-two on both sides.
So we have f minus thirty-two equals nine-fifths times c,
and now we can multiply both sides by the reciprocal of nine-fifths,
which would be five-ninths.
This simplifies to one c, or c,
and then we have five-ninths times f, minus thirty-two,
and let's go ahead and switch this around.
Celsius is going to be equal to five-ninths times
the quantity f, minus thirty-two.
And sometimes it may be helpful to write this in the form of
five times the quantity f, minus thirty-two all divided by nine.
So this would be a more convenient formula to convert fahrenheit to celsius.
Let's take a look at a couple of examples.
So to convert twenty-five degrees celsius to fahrenheit,
we'll substitute twenty-five for c, to determine f.
So I'll write twenty-five over one,
and notice how we can simplify here, there's one factor of five here,
and five factors of five there.
So we'd have nine times five, that's forty-five,
plus thirty-two,
so we're going to have seventy-seven degrees fahrenheit.
Let's take a look at one more example here.
We want to convert seven degrees celsius to fahrenheit,
so we'll have nine-fifths times seven over one, plus thirty-two.
Now this isn't going to simplify this time, so we'll have
sixty-three fifths plus thirty-two.
Let's go ahead and convert sixty-three fifths to a decimal.
So we'll have sixty-three divided by five,
so we'll have twelve, point, six plus thirty-two,
which would be forty-four, point, six degrees fahrenheit.
Now let's convert fahrenheit to celsius.
So again we have two forms of the equation that we can use.
To convert fifty-nine degrees fahrenheit to celsius,
we'll substitute fifty-nine for f.
Fifty-nine minus thirty-two is twenty-seven, so I'll write twenty-seven over one.
And again this one simplifies nicely. There's one factor of nine here,
and three factors of nine there,
so we have fifteen degrees celsius.
And for the last example,
we'll convert ninety-two degrees fahrenheit to celsius.
So we'll have five-ninths times ninety-two, minus thirty-two,
which is five-ninths times sixty, or sixty over one.
Now there's a common factor of three here.
There are three, threes in nine and there are
twenty-threes in sixty.
This would be one hundred divided by three,
and we'll go ahead and use the calculator.
So it's thirty-three, point, three repeating.
Let's go ahead and round this to the nearest tenth.
This would be approximately thirty-three, point, three degrees.
And that's going to do it for this video.
I hope you found this helpful.