As you recall from
basic
algebra, the slope of a non-vertical line measures the steepness of the
line as related to the x-axis. If two points are on the same line
then the definition of slope is as follows:

Important facts about slope!!

1)
Horizontal lines have a slope = 0.

2)
Vertical lines have
undefined
slope because
the
denominator is zero.

Note: The
blue line has a positive slope because it
goes uphill from left to right. The
red line has a negative slope because it goes downhill from left to
right.
The purple line has an undefined slope
because
it is vertical. The green line has
zero
as the slope because it is horizontal.

Important facts about slope to remember!

1)
The slope of y = mx
+ b
is m. m is always constant for a line.

2)
Two nonvertical lines are parallel if and only if they have the same
slope.

3)
Two lines are perpendicular if and only if their slopes are negative
reciprocals.

Sample problems

1) Find the slope of
the
line thru (4,3) and (5,7).

Solution: m = (7 -
3)/(5
- 4) = 4/1 = 4 Make sure you subtract in the same order.

2) Find the slope of
the line
thru (4,5), (4,3).

Solution: m = (5 -
3)/(4
- 4) = 2/0 = undefined. The line is vertical

3) Find the slope of
the line
with the equation y = 4x + 5

Solution: It is in
the
correct form so the slope is m = 4

4) Find the slope of
the line
with the equation 4x + 2y = 8

Solution: The
equation
needs to be placed in the correct form. 2y = -4x + 8 y = -2x + 4

Therefore, the slope m
= -2.
The line is going downhill.

5) y = 4x +
7,
y = 4x - 3, y = (-1/4)x + 8. Tell which
are
parallel and which are perpendicular.

Solution: The first
and
second are parallel because they have the same slope, while the third
equation
is perpendicular to the first two because the slope is a negative
reciprocal.