Answer:
[tex]y < -\frac{3}{2}x+1[/tex]
Step-by-step explanation:
Given:
From the graph shown,
The broken line means that the inequality sign will be either < or >.
The shaded region is to the left of the broken line. This means that [tex]y < f(x)[/tex].
Now, in order to find equation of line, we need slope and y-intercept.
From the graph, the y intercept is at [tex](0,1)[/tex]. So, y intercept is 1.
Also, if we consider two points [tex](0,1)\textrm{ and }(2,-2)[/tex] on the line, then slope is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-2-1}{2-0}=\frac{-3}{2}=-\frac{3}{2}[/tex]
Therefore, the equation of the line is given as:
[tex]y=mx+b\\y=-\frac{3}{2}x+1[/tex]
But as the shaded region is to the left of the line,
∴ [tex]y<-\frac{3}{2}x+1[/tex] is the correct answer.
