Answer:
Option 2
Step-by-step explanation:
Given : Inequality [tex]3y-2x>-18[/tex]
To find : Which shows the graph of the solution set of given inequality?
Solution :
First, We find the x and y-intercepts and connect these two dots by extending infinitely from both sides.
For x-intercept put y = 0,
[tex]3(0)-2x=-18[/tex]
[tex]x=9[/tex]
Point is (9,0)
For y-intercept put x= 0,
[tex]3y-2(0)=-18[/tex]
[tex]y=-6[/tex]
Point is (0,-6)
Next, we test the inequality by choosing a random data point that does not coincide with any of the data points passed by the line.
Let, we choose the origin (0,0)
[tex]3y-2x>-18[/tex]
[tex]3(0) - 2(0) > -18[/tex]
[tex]0> -18[/tex]
The inequality is true for (0,0).
Thus, the shaded region must include this point.
i.e, All of the region to the left bounded by the line is a solution.
The data points are hollow because they are not part of the solution as the inequality is '>'. If it were ≥, then those points would be solid.
Referring to above points the graph showing inequality is Option 2.
Refer the attached graph below.
