Question

the graph below represents which system of inequalities? A y<-2x+6 y<= x+2B y<=-2x+6 y=2x+2D None of the above

Answer 1

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

`m=(y2-y1)/(x2-x1)=(2-0)/(0-(-2))=(2)/(2)=1`

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:

`m=(y2-y1)/(x2-x1)=(6-0)/(0-3)=(6)/(-3)=-2`

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.