Question

Which point is a solution to the inequality shown in this graph

Answer 1

a solution would be (0,5)

it cannot be (3,3) or (-3,-1) because u have a dashed line...and it cannot be (0,0) because that is not in the solution area either

Answer 2

Step 1

Find the equation of the line of the inequality

Let

`A(-3,-1)\ B(3,3)`

Find the slope of the line

The slope is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(3+1)/(3+3)`

`m=(4)/(6)`

`m=(2)/(3)`

Find the equation of the line into point-slope form

`y-y1=m(x-x1)`

we have

`m=(2)/(3)`

`(x1,y1)=B(3,3)`

substitute in the equation

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

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

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

Find the equation of the inequality

The solution is the shaded area above the dotted line

so the inequality is

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

If a point is the solution of the inequality, then it must satisfy the inequality. Let's check each of the points

Step 2

case A)
`(0,0)`

Substitute the values of x and y in the inequality

`x=0\ y=0`

`0>(2)/(3)*0+1`

`0>1`-----> is not true

therefore

the point
`(0,0)` is not solution of the inequality

Step 3

case B)
`(3,3)`

Substitute the values of x and y in the inequality

`x=3\ y=3`

`3>(2)/(3)*3+1`

`3>3`-----> is not true

therefore

the point
`(3,3)` is not solution of the inequality

Step 4

case C)
`(-3,-1)`

Substitute the values of x and y in the inequality

`x=-3\ y=-1`

`-1>(2)/(3)*-3+1`

`-1>-1`-----> is not true

therefore

the point
`(-3,-1)` is not solution of the inequality

Step 5

case D)
`(0,5)`

Substitute the values of x and y in the inequality

`x=0\ y=5`

`5>(2)/(3)*0+1`

`5>1`-----> is true

therefore

the point
`(0,5)` is a solution of the inequality

therefore

the answer is

`(0,5)`