How do you graph the linear inequality #-2x - 5y<10#?

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{(x^2+(y+2)^2-0.05)((x+5)^2+y^2-0.05)(-2x-5y-10)=0 [-10, 10, -5, 5]}

Now, we can shade the rightside of the line.

The boundary line will need to be changed to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(-2x-5y-10) < 0 [-10, 10, -5, 5]}

To graph the linear inequality -2x - 5y < 10, first graph the boundary line -2x - 5y = 10 (the line formed by replacing the inequality symbol with an equal sign). Then, choose a test point not on the boundary line and substitute its coordinates into the original inequality to determine whether the region above or below the line is shaded. Finally, shade the appropriate region.