Which inequality is represented by this graphy \geqslant - (1)/(6) x + 1y \leqslant - (1)/(6) x + 1y \ \textless \ - (1)/(6) x + 1y \ \textgreater \ - (1)/(6) x + 1

Question

Which inequality is represented by this graph
`y \geqslant - (1)/(6) x + 1`
`y \leqslant - (1)/(6) x + 1`
`y \ \textless \ - (1)/(6) x + 1`
`y \ \textgreater \ - (1)/(6) x + 1`

Answer 1

`\begin{gathered} (x1,y1)=(0,1) \\ (x2,y2)=(6,0) \\ \text{the slope is:} \\ m=(y2-y1)/(x2-x1)=(0-1)/(6-0)=-(1)/(6)_{} \end{gathered}`

Using the point-slope equation:

`\begin{gathered} y-y1=m(x-x1) \\ y-1=-(1)/(6)x-0 \\ y=-(1)/(6)x+1 \end{gathered}`

since the values are above the line:

`y>-(1)/(6)x+1`