Question

This graph shows the solution to which inequality

Answer 1

Option B -
`y>(1)/(3)x-2`

Explanation:

Given : The graph attached.

To find : This graph shows the solution to which inequality ?

Solution :

The graph is passing through points (-3,-3) and (3,-1).

Applying two point slope form to get the equation of line,

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

Here,
`(x_1,y_1)=(-3,-3)` and
`(x_2,y_2)= (3,-1)`

Substitute in the formula,

`y-(-3)=(-1-(-3))/(3-(-3))(x-(-3))`

`y+3=(2)/(6)(x+3)`

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

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

`y=(1)/(3)x-2`

Now we see that the line approach towards origin and above the line so inequality sign is greater.

As line is dotted line so it is not equality.

The required inequality is
`y>(1)/(3)x-2`

Therefore, option B is correct.

Answer 2

The correct option is B.

Explanation:

From the given graph it is clear that the related line passing through the points (-3,-3) and (3,-1).

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-(-3)=(-1-(-3))/(3-(-3))(x-(-3))`

`y+3=(2)/(6)(x+3)`

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

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

`y=(1)/(3)(x)+1-3`

`y=(1)/(3)(x)-2`

The equation of related line is
`y=(1)/(3)(x)-2`.

Since the related line is dashed and the shaded region is above the line, therefore the sign of inequality is >.

The graph shows the solution to inequality

`y>(1)/(3)(x)-2`

Therefore the correct option is B.