You can put this solution on YOUR website!
the celsius temperature shows the freezing point at 0 degrees and the boiling point at 100 degrees.
the fahrenheit temperature shows the freezing point at 32 degrees and the boiling point at 212 degrees.
at the freezing point, the fahrenheit temperature is equal to the celsius temperature + 32 degrees.
if we let x equal to celsius temperature and we let y equal the fahrenheit temperature, and we assume a linear equation is suffiicient to model the relationship, then our formula will be:
y = mx + 32
y is the fahrenheit temperature and x is the celsius temperature.
when x is equal to 0, y is equal to 32 degrees.
that's the fahrenheit temperature when the celsius temperature is 0 degrees.
when x = 100, we know that y is equal to 212 degrees.
y = mx + b is the slope intercept form of a straight line.
m is the slope.
b is the y intercept.
we already found b = 32 because we know that when x is equal to 0, y is equal to 32.
that led to y = mx + 32
we now need to find m (the slope).
the slope is determined by the following equation:
m = slope = (y2-y1) / (x2 - x1)
(x1,y1) is one point on the line of the equation.
(x2,y2) is the other point on the line of the equation.
our first point is equal to (x1,y1) which is equal to (0,32).
that's the point where celsius (x) is equal to 0 and fahrenheit (y) is equal to 32 degrees.
our second point is equal to (x2,y2) which is equal to (100,212).
that's the point where celsius (x) is equal to 100 and fahrenheit (y) is equal to 212 degrees.
the slope is therefore equal to (y2 - y1) / (x2 - x1) which is equal to (212 - 32) / (100 - 0) which is equal to 180 / 100 which is equal to 18 / 10 which is equal to 9 / 5.
our slope is equal to 9/5.
our y intercept is equal to 32.
out equation is y = 9/5 * x + 32.
if you know the celsius temperature, then use this formula to find the equivalent fahrenheit formula.
if you know the the fahrenheit temperature, then the formula to find the celsius temperature is derived from this formula as follows:
start with y = 9/5 * x + 32
subtract 32 from both sides of this equation to get:
y - 32 = 9/5 * x
multiply both sides of this equation by (5/9) to get:
5/9 * (y - 32) = x
this is the equation to convert from fahrenheit to celsius.
to convert from celsius to fahrenheit, the equation is:
y = 9/5 * x + 32
to convert from fahrenheit to celsius, the equation is:
x = 5/9 * (y - 32)
to test this out, assume the celsius is 0 degrees.
to convert to fahrenheit, the formula becomes:
y = 9/5 * 0 + 32 which results in y = 32
to convert 32 degrees fahrenheit to celsius, the formula becomes:
x = 5/9 * (y - 32) which results in x = 5/9 * 0 which results in x = 0.
on the other end, assume the celsius is 212 degrees.
to convert to fahrenheit, the formula becomes:
y = 9/5 * 100 + 32 which results in y = 180 + 32 which results in y = 212.
to convert 22 degrees fahrenheit to celsius, the formula becomes:
x = 5/9 * (212 - 32) which results in x = 5/9 * 180) which results in x = 100.
the formula works at the extremes that we used to derive the formula in the first place.
it will work in between as well.
bear in mind that the celsius to fahrenheit conversion is not necessarily a straight line function, so the estimates in between will be close to the actual temperature but not exactly on.
assume celsius is 50 degrees.
fahrenheit is equal to 9/5 * 50 + 32 which is equal to 122 degrees.
the actual fahrenheit temperature will be near 122 degrees but not necessarily right at 122 degrees.
the formula will give you an approximation that is close but will not necessarily be right on.
as far as the equation you showed up top in your problem, i don't understand what that has to do with celsius or fahrenheit.
the equation is:
x+10y=2, for y
it appears you want to solve for y.
here's how you would do that:
x + 10y = 2
subtract x from both sides of the equation to get:
10y = -x + 2
divide both sides of the equation by 10 to get:
y = (1/10) * -x + (1/10) * 2
this is equivalent to:
y = -(1/10)x + (1/5)
your original equation is x + 10y = 2
after you solved for y, your final equation is y = (-1/10)x + (1/5)
take any value for x and solve for y in the second equation.
use those values for x and y in the first equation and you'll see that it becomes a true equation which will confirm the final equation as being a good one.
i assumed x was equal to 32.
i chose this number at random.
i substituted for the value of x in the second equation to get;
y = (-1/10) * 32 + (1/5) to get y = -3
i substituted for x and y in the first equation to get:
x + 10 y = 2 becomes 32 + (10 * -3) = 2 which becomes:
32 - 30 = 2 which becomes 2 = 2
this equation is true so the value of 32 for x and -3 for y is good.
the equation is true means that the values of x and y that we used are solutions to the equation.