Question

Which inequality is represented by this graph$y \geqslant - \frac{1}{6} x + 1$$y \leqslant - \frac{1}{6} x + 1$$y \ \textless \ - \frac{1}{6} x + 1$$y \ \textgreater \ - \frac{1}{6} x + 1$

Answer 1

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

Using the point-slope equation:

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

since the values are above the line:

$y>-\frac{1}{6}x+1$