Answer
See below:
Work Step by Step
Graph each inequality on the same plane.
Step 1: Convert the inequality to an equation by replacing inequality by = sign.
Equation 1: \[4x+6y\le 24\]
\[4x+6y=24\]
Equation 2: \[y>2\]
\[y=2\]
Step 2: Graph the equation using intercept form or slope-intercept form.
Equation 1: \[4x+6y\le 24\]
Make \[x=0\] to find the y-intercept,
\[\begin{align}
& 4x+6y=24 \\
& 0+6y=24 \\
& y=4
\end{align}\]
Make \[y=0\] to find x-intercept,
\[\begin{align}
& 4x+6y=24 \\
& 4x+0=24 \\
& x=6
\end{align}\]
The line passes through \[\left( 0,4 \right)\] and\[\left( 6,0 \right)\]. The line is solid since the inequality contains the ≤ symbol.
Equation 2: \[y>2\]
The equation does not contain x. For any value of x, y is constant. The graph will be parallel to the x-axis.
The line passes through \[\left\{ \ldots \left( -1,-2 \right),\left( 0,-2 \right),\left( 1,-2 \right)\ldots \right\}\]
The line is dashed since the inequality contains > symbol.
Choose a test point for\[4x+6y\le 24\]. The origin \[\left( 0,0 \right)\]be the test point. Substituting in the inequality
\[0\le 24\]
The statement is true. The graph contains the test point.
