How do you graph x+2y<-2 in linear inequality form

Question

How do you sketch this linear inequality on a graph x+2y<-2 ?

 

 

Answer 1

First it should be converted so that we solve for y like your standard graphs:

x - y > -1

Subtract x from both sides:

-y > -x - 1

Now we divide by -1. Note that when we divide by a negative, the inequality sign flips as well. Don't let your graph get messed up by a simple oversight.

y < x + 1

 

Now it looks mostly like a graphing linear equation, right? The thing to keep in mind is that < sign. That means that when you graph it, you use a dashed line instead of a solid line since the value is not equal to the equation (if it were a ≤ sign, then it would be solid to denote the "equals" part).

 

The other part to note is that since the sign denotes "less than," then that means any value of x below that line works as well, so you need to shade in the part of the graph below the dashed line.

Examples:

 (3, 0) 0 < 3 + 1 true

 (0, 0) 0 < 0 + 1 true

(-1, 0) 0 < -1 + 1 false (but that's why we use the dashed line)

(-2, 0) 0 < -2 + 1 false, so it's not a value that works