Question

Represent to solution set of each of the following in equations graphically in two dimensional plane :

y>2x-8

Answer 1

we have,

y>2x-8 ...(i)

Converting the inequation into equation,we obtain,y=2x-8

Putting x=0, we get y=-8

Putting y=0, we get x=$\frac{8}{2}=4$

So, this line meets x-axis at (4,0) and y-axis at (0,-8).

we plot these points and join them by a thick line. This line divides the xy-plan in two parts. To determine the region represented by the given inequality consider the point 0(0,0).

Putting x=0,and y=0 in the in equation (i),we get,$0\ge -8$

Clearly,(0,0) satisfies the inequality. So, the region containing the origin is represented by the given in equation as shown below: