Question

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 3) and (3, 1). Everything below and to the right of the line is shaded.

Which linear inequality is represented by the graph?

y > Two-thirdsx – 2
y < Two-thirdsx + 2
y > Two-thirdsx + 1
y < Two-thirdsx – 1

Answer 1

y < Two-thirdsx – 1

Explanation:

Answer 2

y < 2/3x - 1

Explanation:

Find the Equation of the line

P1(-3,-3) P2 (3,1)

1.) Find the Slope

Rise: 1-(-3) = 4

Run: 3-(-3) = 6

m =
`(Rise(Changeiny))/(Run(Changeinx))` =
`(4)/(6)`=
`(2)/(3)`

2.) Find y intercept (B)

y = 2/3x + b

-3 = 2/3(-3) + b <-Plug a point in

-3 = 2 + b

-2 -2

-1 = b

3.) Equation

y = 2/3x - 1

Write an inequality

Since y must be below the line, that means y is less than the equation used to find the line.

y < 2/3x - 1

Though I was not able to get the right answer I'll just answer what has the right equation.