Question

graph the linear inequality. y > 3x + 4 use the graphing tool to graph the inequality. click to enlarge graph

Explanation:

Step1: Identify the boundary - line

The boundary - line of the inequality $y>3x + 4$ is the equation $y = 3x+4$. This is a linear equation in slope - intercept form $y=mx + b$, where $m = 3$ (the slope) and $b = 4$ (the y - intercept).

Step2: Determine the type of the boundary - line

Since the inequality is $y>3x + 4$ (strict inequality), the boundary - line $y = 3x+4$ will be a dashed line.

Step3: Test a point

Choose a test point not on the line. The origin $(0,0)$ is a convenient choice. Substitute $x = 0$ and $y = 0$ into the inequality $y>3x + 4$. We get $0>3(0)+4$, or $0>4$, which is false.

Step4: Shade the region

Since the test point $(0,0)$ does not satisfy the inequality, we shade the region that does not contain the origin. That is the region above the dashed line $y = 3x+4$.

Answer:

Graph a dashed line $y = 3x+4$ (using the y - intercept at $(0,4)$ and slope of 3) and shade the region above the line.