Graph the linear inequality.
\[
y> 3 x+2
\]
Use the graphing tool to graph the inequality.
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Answer
\(\boxed{\text{The graph of the inequality } y > 3x + 2 \text{ is a region in the coordinate plane above the dashed line } y = 3x + 2. \text{ The line is dashed to indicate that points on the line are not included in the solution. The region is shaded to indicate that any point in that region is a solution to the inequality.}}\)
Step 1 ：First, we need to graph the line \(y = 3x + 2\). This line will be a boundary for the inequality. Since the inequality is 'greater than' and not 'greater than or equal to', the line will be dashed to indicate that points on the line are not included in the solution.
Step 2 ：The line \(y = 3x + 2\) has a slope of 3 and a y-intercept of 2. So, we start at the point (0,2) on the y-axis and move up 3 units and over 1 unit to the right to plot additional points.
Step 3 ：After graphing the line, we need to determine which side of the line to shade. Since the inequality is \(y > 3x + 2\), we shade the area above the line.
Step 4 ：\(\boxed{\text{The graph of the inequality } y > 3x + 2 \text{ is a region in the coordinate plane above the dashed line } y = 3x + 2. \text{ The line is dashed to indicate that points on the line are not included in the solution. The region is shaded to indicate that any point in that region is a solution to the inequality.}}\)
