Question

Part A: Explain how to determine if the boundary line of a linear inequality should be solid or dashed when graphed on acoordinate plane.Part B: Explain how the test point (0,0) can be used to determine which half plane should be shaded for the linearinequality 3x +y > 4. Show all work.Part C: Describe how to graph the linear inequality y > 2x – 1 on a coordinate plane.

Answer 1

Part A:

It depends on the signs:

The line is solid if:

The inequality involves a greater equal or a lesser equal.

example:

`\begin{gathered} x+y\ge1 \\ or \\ x+y\le1 \end{gathered}`

The line is dashed if:

Inequality involves a greater than or less than.

example:

`\begin{gathered} 5x+2<10 \\ or \\ 5x+2>10 \end{gathered}`

This is because when we speak of a strict greater or lesser. the area does not touch the boundary line. While in the opposite case if it touches the border line.

Part B:

Let's evaluate the point (x,y) = (0,0):

`\begin{gathered} 3x+y>4 \\ x=0,y=0 \\ 0+0>4 \\ 0>4 \\ This_{\text{ }}is_{\text{ }}false \\ 0<4 \end{gathered}`

We can conclude that this point is not a solution for the inequality, so, it does not belong to the solution region:

Part C:

Let's focus on graph the equivalent line:

`\begin{gathered} y=2x-1 \\ \end{gathered}`

From this equation we can see:

`\begin{gathered} m=2 \\ b=-1 \\ y-\text{intercept}=(0,-1) \\ x-\text{intercept}=(0.5,0) \end{gathered}`

since it is greater than (>), the line is dashed and the shaded region is above the line: