Question

Algebra 1 Write a system of inequalities to represent the shaded portion of the graph.

Answer 1

Given: A shaded portion of the graph

Required: System of inequalities to represnt the shaded portion.

Step-by-step explanation:

Firstly consider the the non-dotted line.

It passes through two points. (0,3) and (-1.5,0)

So write the equation of line using two point form.

`\begin{gathered} y-3=(3-0)/(0-(-1.5))(x-0) \\ y-3=2x \end{gathered}`

so the equation is

`2x-y+3=0`

Since (0,0) lies in shaded region, therefore the inequality is

`2x-y+3\ge0`

Now, consider the dotted line.

It passes through two points. (-3,0) and (0,-1).

Equation of dotted line is

`\begin{gathered} y-0=(0-(-1))/(-3-0)(x+3) \\ y=-(1)/(3)(x+3) \end{gathered}`

So the equation is

`\begin{gathered} 3y=-x-3 \\ x+3y+3=0 \end{gathered}`

Now, since (0,0) lies in the shaded portion, therefore the inequality is

`x+3y+3>0`

Final Answer: The system of inequalities are

`\begin{gathered} 2x-y+3\ge0 \\ x+3y+3>0 \end{gathered}`