ANSWER
Therefore the correct answer is B
<u>EXPLANATION</u>
The equation in the point slope form of a straight line is given by the formula;
, where
is the slope and the point
is any point on the line.
Since two points on the line are given, Lamont must find the slope using the points and
as follows;
.
He can now choose one of the points as .
If he uses , the he obtains,
Which gives as the equation of the line.
Therefore the correct answer is B
1. Start the search among 2-digit numbers. A dropdown number (DDN) with 2 digits is a number such that
or
but both of these solutions violate the requirement that the digits are distinct, so there are no 2-digit DDNs.
A 3-digit DDN is such that
or if the average is
, or
if the average is
. The smallest possible value for
is 1 since we require 3 digits. Then
, and we can pick
and
to get the smallest DDN, 102.
2. In a 4-digit DDN , we have
or or
or
.
We're free to fix and
to try to get the smallest DDN. This leaves us with
or
or
or
.
The first two cases are impossible - the only choices for such that
are 1 and 2, and the sum of two positive integers must be positive. The smallest possible value of
is 2; this leaves us with
or
, but the latter case is impossible because 3 does not divide 2. So
, and the <em>smallest</em> 4-digit DDN is 1025.
To find the largest DDN, start with the largest possible values for and
. Let
and
. Then
or
or
or
. At most, we can have
with 7 and 6, so the first two cases are impossible. If we maximize
, then either
or
(which we don't want). So the <em>largest</em> 3-digit DDN is 9874.
3. I don't have an analytical solution to this, but using brute force (program) the total count is 112.
4. It is possible; consider 1249 and 1250, with digital averages
which happens to be the smallest pair. (Also found with brute force.)