Slope
When we use a rule to plot a line onto a Cartesian Plane we can determine its
slope a few different ways. The SLOPE is the steepness of a line between
two or more coordinates. Remember that when we use a rule the line on the
Cartesian Plane will always be a straight line. This means that the slope will
be the same between any two points.
**Note that a slope can be positive or negative
Finding the Slope from a Graph (Cartesian Plane)
To find the slope from two coordinates on a Cartesian Plane we must find
the number of units for both the x-axis and the y-axis. We put this
information into a fraction by doing the following:
1. Begin at the left coordinate (dot)
2. Count the number of units it takes to reach the other coordinate
along the x-axis (it will always be towards the right so the number will
always be positive).
3. Make this number the denominator.
4. Count the number of units it takes to reach the other coordinate
along the x-axis (if you move up on the graph it is positive; if you move
down it is negative).
5. Make this number the numerator.
6. Reduce fraction if possible.
Example:
There are 4 units along the x-axis so "4" is
our denominator.
There are 3 units going up so positive "3" is
our numerator.
Therefore our slope is 4/3 (always reduce
the fraction if possible)
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Finding the Slope from a Rule
The form of a rule is y = mx + b where m is the slope. We will ignore the b
for now. To find the slope we simply take the number before the 'x'.
Example:
If the rule
If the rule
If the rule
If the rule
is
is
is
is
y = 2x + 4 the slope is 2.
y = -3x the slope is -3.
y = 2/3x – 7 the slope is 2/3
y = -0.75x + 1 the slope is -0.75
Finding the Slope from a Table of Values
We can also find the slope from a table of values. To do this we find the
difference (subtraction) between two x-coordinates and the same two ycoordinates. We put this information into a fraction to find the slope.
Example:
x
y
1. Find the difference between two x-coordinates from the
-1
-6
table to the right. From our example, the difference is +1.
0
-4
2. Find the difference between the corresponding two y
1
-2
coordinates. From our example, the difference is +2.
2
0
3. Put these into a fraction with the form y/x – this means
that our fraction is 2/1.
4. Reduce the fraction (if possible) – 2/1 = 2, therefore the slope is 2.