c = w*45/13 + 60/13
I will be assuming that the equation will be linear since there are only 2 data points available. The form of the equation will be
c = aw + b
where
c = calories burned
a = some constant
w = weight
b = some other constant.
If you look at the equation, you'll notice that it looks like the equation for a line i slope intercept form. So first, let's calculate the slope of the desired equation.
a = (600-420)/(172-120) = 180/52 = 45/13 = 3.461538462
Now we have the equation
c = w*45/13 + b
Substitute the values for a known point, giving
420 = 120*45/13 + b
Now solve for b
420 = 120*45/13 + b
420 = 5400/13 + b
420 - 5400/13 = b
5460/13 - 5400/13 = b
60/13 = b
So now the equation is
c = w*45/13 + 60/13
