Question

Which is the graph of the linear inequality 1/2 x – 2y > –6? Image for option 1 Image for option 2 Image for option 3 Image for option 4

e.d.g.e.n.u.i.t.y

Answer 1

I think it is D.

I could be wrong though, my apologies if I am :(

Answer 2

The graph in the attached figure

Explanation:

we have

`(1)/(2)x-2y > -6`

Isolate the variable y

`-2y > -6-(1)/(2)x`

Divide by -2 both sides

`y < 3+(1)/(4)x`

The solution of the inequality is the shaded area below the dashed line
`y = 3+(1)/(4)x`

To plot the inequality find the intercepts

The y-intercept is the point (0,3) (value of y when the value of x is equal to zero)

The x-intercept is the point (-12,0) (value of x when the value of y is equal to zero)

Plot the intercepts

Drawn the dashed line

shaded the region below the dashed line

The graph in the attached figure