how do you write the slope if the run is 1/2

Question

I am putting into point slope formula, the rise is 1 and the run is 1/2.  how do I write the slope if the run is a fraction?

Answer 1

When you have a fraction in the denominator, you invert it (change 1/2 to 2/1) and multiply:

 

 1        1      2

---  =  --- * ---  =  2

1/2      1      1

 

A second way to think of it is that 1 is twice as big as 1/2, so the ratio 1/(1/2) = 2.

 

A third way to do it is to multiply the numerator and denominator by the reciprocal of the fraction.  The reciprocal of 1/2 is 2/1 = 2, and (1/2)*2=1:

 

 1        1        2      2
--- = ------ * --- = --- = 2
1/2   (1/2)     2      1

 

All three ways are equivalent.