Observe the graph:
\Consider the end points of the triangle on the graph are
and
.
Find the first inequality.
\Points are
and
.
Find the slope.
\
(Slope formula)
(Substitute
and
)
(Multiply)
(Add)
(Simplify)
Find the slope intercept line equation.
\The slope intercept line equation is
.
(Slope intercept formula)
(Substitute
and
)
(Multiply)
(Subtract
from each side)
(Apply additive inverse property:
)
Write a system of inequality.
\The points are
and
and line equation is
.
The shaded region is above the line equation and it represent the solid line.
\Hence, the inequality is
.
Find the second inequality.
\Points are
and
.
Find the slope.
\
(Slope formula)
(Substitute
and
)
(Add)
(Simplify)
Find the slope intercept line equation.
\The slope intercept line equation is
.
(Slope intercept formula)
(Substitute
and
)
(Multiply)
(Add
to each side)
(Apply additive inverse property:
)
Write a system of inequality.
\The points are
and
and line equation is
.
The shaded region is below the line equation and it represent the solid line.
\Hence, the inequality is
.
Find the third inequality.
\Points are
and
.
Find the slope.
\
(Slope formula)
(Substitute
and
)
(Multiply)
(Add)
(Simplify)
Find the slope intercept line equation.
\The standard form of slope intercept line equation is
.
(Slope intercept formula)
(Substitute
and
)
(Multiply)
(Subtract
from each side)
(Apply additive inverse property:
)
Write a system of inequality.
\The points are
and
and line equation is
.
The shaded region is above the line equation and it represent the solid line.
\Hence, the inequality is
.
The inequalities are
,
and
.