Algebraic Manipulation Worksheets With Answers - Craven Community College Page 19
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29Example: Graph 3X – 4Y < 12
1. Graph the related line.
The line is plotted dashed.
2. Choose the point (0, 0) and check these
values in the original inequality.
3(0) – 4(0) < 12
0 < 12.
Note: If (0, 0) is on the boundary, select
another point such as (0, 1) or (1, 0) not on
the boundary.
3. Shade the half-plane containing (0, 0)
Note: If the point tested produces a false
statement, shade the half-plane that does not
contain the tested point.
Slope of a Line
Slope is a measure of the steepness of a line. Slope is defined by the formula:
Slop = m = change in Y
change in X
Slope is calculated using the formula:
m = Y
– Y
2
1
X
– X
2
1
When (X
, Y
) are the coordinates from point 1 and (X
, Y
) are the coordinates from the point 2. It
1
1
2
2
should be noted that it does not matter in which order the two points are considered. The labeling of point
1 and point 2 is arbitrary, as long as both coordinates represent the point labeled as point 1 are used as X
1
and Y
and both coordinates representing the point labeled as point 2 are used as X
and Y
. Furthermore
1
2
2
it does not matter which two points on any given line are used to determine the slope, the slope remains
the same regardless of the point chosen to compute it.
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