Question

This graph shows the solution to which inequality (3 3) (-3 -1)

Answer 1

`\boxed{y > (2)/(3) x + 1}`

Option B is the correct option.

Explanation:

point ₁ ( - 3 , - 1 ) x₁ = - 3 , y₂ = - 1

point ₂ ( 3 , 3 ). x₂ = 3 , y₂= 3

Now, let's find the slope:

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

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

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

`= (4)/(6)`

`= (2)/(3)`

At ( 3 , - 1 )

y = mx + c , where m is the gradient / slope amd c is called the intercept on y-axis

`- 1 = (2)/(3) * ( - 3) + c`

Solve for c

`- 1 + 2 = c`

`c = 1`

Since, The red line is dotted line. Therefore it does not include the equal to part. And the shaded region is upper part. Hence, ' > ' should be used.

The answer would be:

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

Hope I helped!

Best regards!

Answer 2

B

Explanation:

since the graph shows dotted line the sign has to be < or > so C and D eliminated from your answer

y>2/3 x +1 is your answer (B)