Question

Two-Variable inequalities from their graph. (1,0) and (0,1) Find the inequalities represented by the graph.

Answer 1

$\begin{gathered} Let \\ \mleft(x1,y1\mright)=\mleft(0,-1\mright) \\ (x2,y2)=(1,0) \\ \end{gathered}$

Let's find the slope of the line:

$\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{0-(-1)}{1-0}=\frac{1}{1}=1 \\ \end{gathered}$

Using the point-slope equation:

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

since the line is not dashed, and the area is below the line:

$y\le x-1$