Answer:
C. \(y<-\frac{1}{2}x-4\)
Step-by-step explanation:
We have been given graph of an inequality. We are asked to find inequality graphed below.
First of all, we will find boundary line of our given inequality.
We can see that y-intercept is \(-4\).
Slope: \(m=\frac{y_2-y_1}{x_2-x_1}\)
Use points: \((0,-4)\text{ and }(-8,0)\)
\(m=\frac{0-(-4)}{-8-0}\)
\(m=\frac{0+4}{-8}\)
\(m=\frac{4}{-8}\)
\(m=-\frac{1}{2}\)
Therefore, the equation of boundary line would be \(y=-\frac{1}{2}x-4\).
Since boundary line is dotted, so points on one side of boundary line would be \(y>-\frac{1}{2}x-4\) and points on other side would be \(y<-\frac{1}{2}x-4\).
Let us check point (0,0) to find the correct region.
\(y<-\frac{1}{2}x-4\)
\(0<-\frac{1}{2}(0)-4\)
\(0<0-4\)
\(0<-4\)
We can see that the shaded region in given inequality doesn't include point (0,0), therefore, our required inequality is \(y<-\frac{1}{2}x-4\).
