2. Slope of a Line
The Formula that applies when calculating the slope of
a line: Slope = Rise/Run
In the following graph
the slope of the lines
can all be calculated
independently using this
formula.
3. For example, lets look at line
CD. The rise is equal to 2, and
the run is equal to 4. Using
the formula “slope = rise/run”
we can calculate that the
slope is 2/4, or ½.
Using this same method I will
calculate the rest of the lines:
AB = 0
BC = 2
CD = ½
DE = 3/2
EF = -1/2
4. • The steepest line is the line BC, with a slope of 2. If you
look at the earlier calculations I did you can see that
none of the other lines have as great a slope.
• The line AB is the least steep. In fact it is perfectly
horizontal, having no rise. Using the formula given
earlier we can see that the slope of line AB = 0/6 which
is equal to 0.
• The lines CD and EF look very similar having the same
rise an run. However, when the slope is decreasing
from left to right instead of increasing, the slope has to
be negative. Therefore, the slope CD = ½ while the
slope EF = -1/2. It is a very slight distinction that is easy
to forget, but the two lines are actually very different.
5. • The slope of CD is ½ and the slope of BC is 2. The
graph I have drawn has a rise of 6 and a run of
6, putting the slope at 1, which is steeper than CD
but not as steep as BC.
6. Representing Relations
Given the letters in the square below I was asked to
come up with words that were longer than three
letters, each contained a T, and never used plurals or
the same letter twice.
Using these words I created a table demonstrating the
relations between the words and the letters. The
following table uses the association “Is a letter of the
word”.
7. Letter Word
A Ate
A Art
A Eat
A Ear
A East
A Rate
A Rat
A Seat
A Sat
A Stare
A Tear
A Tar
A Tea
A Tare
Letter Word
A Taser
E Ate
E Eat
E Ear
E East
E Rate
E Seat
E Stare
E Tear
E Tea
E Tare
E Taser
R Art
R Ear
Letter Word
R Rate
R Rat
R Stare
R Tear
R Tar
R Tare
R Taser
S East
S Seat
S Sat
S Stare
S Taser
8. • If the order of pairs were reversed the table would look
something like this:
• This chart appears at first glance to be fine, however,
the association we were using was “Is a letter in the
word”. To state that “East” is a letter in the word “E”
does not makes sense. In order for this table to work, I
word have to change the association used. If the
association were to become “Has the letter” than the
table would become usable again.
Word Letter
Art A
East E
Rate R
Stare T
