Question

On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 1) and (3, 0). Everything above and to the left of the line is shaded.

Which linear inequality is represented by the graph?

y ≤ One-thirdx − 1
y ≥ One-thirdx − 1
y < 3x − 1
y > 3x − 1

Answer 1

Answer: C

Explanation:

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Answer 2

Option B.

Explanation:

A solid straight line passes through (0, -1) and (3, 0)

Slope of the line =
`(y-y')/(x-x')`

=
`(0+1)/(3-0)`

=
`(1)/(3)`

Equation of the line passing through (0, -1) will be

y - y' = m(x - x')

`y+1=(1)/(3)(x-0)`

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

Since this line is solid then there will the sign of (≥ or ≤)

If everything above and to the left of the line is shaded then the inequality will be

`y\geq (1)/(3)x-1`

Therefore, the answer will be option B.
`y\geq (1)/(3)x-1`