__Linear Explorations__

By: Brandie Thrasher

What are linear equations? As
defined by dictionary.com, it is an equation in which the highest degree is the
first power. An example of a linear equation would be:

y = x + 4

LetŐs
take a look at its graph

LetŐs
take a look at the graph that contains the following linear equations:

y = x + 4

y = x + 3

y = x + 2

y = x + 1

y =
x +
0

y = x + (-1)

y = x + (-2)

y = x + (-3)

y = x + (-4)

It
appears that the graphs seem to be somewhat similar. Considering that they are
all in the form of y =
mx +b,
each equation shares the same slope (m value) in which each line will Ňrise and
runÓ the quantity of m. For these equations, our m value is 1.

These
lines also carry another property in regards to sharing the same slope, they
will NEVER intersect, and thus they are deemed as being parallel to one
another.

Also,
b is used to express the point at which the graph will intersect the y-axis. In
each case shown, our graphs intersect the y-axis at each number representing b.

These
conjectures will always hold true for y = x + n.

See ANIMATION