First we have to identify the equation of each line. For the first one (solid line) the equation must be calculated with points (-2,0) and (0,2). (taken from the graph)
The slope of the line must be
[tex]m=\frac{y2-y1}{x2-x1}=\frac{2-0}{0-(-2)}=\frac{2}{2}=1[/tex]
So, the equation of the blue line is y = x + 2 , given that the y-intercept is 2
For the other line, the points to calculate the equation can be (3,0) and (0,6). (from the graph).
The slope would be:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{6-0}{0-3}=\frac{6}{-3}=-2[/tex]
The equation for the second line would be y=-2x + 6 , since the y-intercept is 6.
The dotted line indicates, the points on the second line (y=-2x + 6) are not included , so , the inequality must be y<-2x + 6. On the contrary, the first line is a solid one, it implies the points on that line are included, therefore, the inequality would be y <= x + 2.
Answer is : Option A.
