The equation of the line is 
.
Solution:
The points on the line are (–6, –3) and (4, –5).
Slope of the line:
Point-slope formula:
Subtract 3 from both sides of the equation.
The equation of the line is .
If you're rolling a single cube, then ...
-- There are 6 possible out comes.
-- One of them (5) is a multiple of 5 .
-- The probability of rolling it is (1/6) = <em>16-2/3 %</em> .
If everything is acting perfectly random, then ion 100 rolls,
you'd expect to succeed 16 or 17 times.
If you're rolling a pair of cubes, then ...
-- There are (6 x 6) = 36 possible outcomes.
-- There are seven ways to get a multiple of 5.
(1+4), (4+1), (2+3), (3+2), (4+6), (6+4), (5+5)
-- The probability of rolling one of those is
(7/36) = <em>19-4/9 %</em> .
If everything is acting perfectly random, then in 100 rolls,
you'd expect to succeed 19 or 20 times.
Notice that if
, then
. Recall the definition of the derivative of a function
at a point
:
So the value of this limit is exactly the value of the derivative of
at
.
You have
