Question

Shown here is the graph of which inequality? PLEASE HELPPP!

Answer 1

The required inequality is
`(y)/(7)\leq (x)/(3)+2`.

Explanation:

From the given graph it is clear that the related line passing throguh the points (-6,0) and (0,14).

If a line passing through two points, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The equation of related line is

`y-0=(14-0)/(0+6)(x+6)`

`y=(14)/(6)(x+6)`

`y=(7)/(3)(x+6)`

Divide both sides by 7.

`(1)/(7)y=(1)/(3)(x+6)`

`(y)/(7)=(x)/(3)+2`

The equation of related line is
`(y)/(7)=(x)/(3)+2`.

The relates line is solid line and the shaded region is below the line therefore the sides of inequality is ≤.

Therefore the required inequality is
`(y)/(7)\leq (x)/(3)+2`.