Graphs of Linear Inequalities: example 4.74

First we graph the boundary line $y=\mathrm{-4}x$. It is in slope–intercept form, with $m=\mathrm{-4}\text{and}b=0$. The inequality is $\le$ so we draw a solid line.

Now, we need a test point. We can see that the point $\left(1,0\right)$ is not on the boundary line.

Is $\left(1,0\right)$ a solution of $y\le \mathrm{-4}x$?

The point $\left(1,0\right)$ is not a solution to $y\le \mathrm{-4}x$, so we shade in the opposite side of the boundary line. See Figure 4.35.