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
.