Answer:
A) [tex]y > \frac{2x}{3} +1[/tex]
Step-by-step explanation:
The general form of a straight line is y = mx + c, where m is the slope and c is the y-intercept.
From the graph, we have the end points of the line as (3,3) and (-3, -1).
Using these points, we will find the value of the slope 'm'.
i.e. m = [tex]\frac{-1-3}{-3-3}[/tex]
i.e. m = [tex]\frac{2}{3}[/tex]
So, we get the equation of the line as [tex]y = \frac{2x}{3} +c[/tex].
Now, using any point say (3,3) and the above equation, we will find the value of the y-intercept c.
i.e. [tex]3 = \frac{2*3}{3} +c[/tex].
i.e. c = 1.
Hence, the equation of this straight line is [tex]y = \frac{2x}{3} +1[/tex].
As seen from the graph, the line corresponding this straight line is dotted not solid, this means that the equality sign is not possible. So, we are left with either A or B.
To get the final answer, we will use the 'Origin Test' i.e. substitute the point (0,0) on both A and B. Then,
1. If the inequality is satisfied, the shaded region is towards the origin.
2. If the inequality is not satisfied, the shaded region is drawn away from the origin.
Now in option A, the 'Origin test' fails and the equation is not satisfied and therefore its graph will be drawn away from the origin, which is the case in our problem.
Hence, option A is correct.
