Graphing Linear Inequalities

1
Graphing Linear Inequalities
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Linear Inequalities
When an inequality symbol is present in a linear
equation, the symbol definitions affect the line
and the area of points above or below the line.
The four inequality symbols are . . .
lt
A less than sign (does not include the points
on the line).

A less than or equal to sign (does include the
points on the line).
gt
A greater than symbol (does not include the
points on the line).

A greater than or equal to sign (does include
the points on the line).
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Linear Inequalities
The line is not included and therefore is dashed.
The area of points that are included are below
the line.
The line is included and therefore is solid. The
area of points that are included are below the
line.
The line is not included and therefore is dashed.
The area of points that are included are above
the line.
The line is included and therefore is solid. The
area of points that are included are above the
line.
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Graphing Linear Inequalities
The y-intercept is at (0, -3) and the slope is
2/1.
Reading from the y, y is less than. This means
that the line is not included and the area of
points that are included are below the line.
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Graphing Linear Inequalities
Reading from the y, y is less than or equal to.
This means that all of the points on the line
are included and the area of points that are
included are below the line.
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Graphing Linear Inequalities
Reading from the y, y is greater than. This
means that the line is not included and the area
of points that are included are above the line.
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Graphing Linear Inequalities
Reading from the y, y is greater than or equal
to. This means that all of the points on the
line are included and the area of points that
are included are above the line.
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Graphing Linear Inequalities
Rewrite in slope-intercept form. add the x
term to both sides of the inequality.
Divide all terms by -3 to create one, positive, y.
Switch the direction of the inequality symbol
when dividing by a negative integer.
Continued on next slide.
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Graphing Linear Inequalities
The y-intercept is at (0, -2) and the slope is -
2/3.
Reading from the y, y is greater than or equal
to. This means the line is solid and the
shading is above the line.