How do you graph the inequality #-5x+2y<-6#?

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

#2y = 4

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+3)^2-0.125)((x-2)^2+(y-2)^2-0.125)(-5x+2y+6)=0 [-20, 20, -10, 10]}

Now, we can shade the left side of the line.

We need to change the boundary to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(-5x+2y+6) > 0 [-20, 20, -10, 10]}

To graph the inequality ( -5x + 2y < -6 ), first graph the boundary line ( -5x + 2y = -6 ) as a dashed line since it's not included in the solution set. Then, choose a test point not on the line, such as (0,0), and substitute its coordinates into the original inequality. If it's true, shade the region containing (0,0); if false, shade the opposite region. Finally, label the shaded region as the solution area.