Question

How to solve and graph? `2x>5y+6`

Answer 1

See below

Explanation:

Let's solve this inequality for `y`:

`2x>5y+6`

`5y<2x-6`

`y<(2x-6)/5=2/5x-6/5`

We can first draw a line (it'll be dotted to represent that the sets of values along the line are not a part of the solution) by graphing the point `(0,-6/5)` which is the `y`-intercept and also point `(0+5,-6/5+2)=>(5,4/5)` and drawing a line through the two points (this first line isn't dotted simply because the editor won't let me - but you want your line to be dotted):

graph{2/5x-6/5 [-2.956, 8.145, -2.393, 3.154]}

And now we need to work out which side of the line is our solution. My favourite point to use for this kind of work is the origin. We plug `(0,0)` to see if the inequality works with this value:

`0<(2(0)-6)/5`

`0<-6/5 color(white)(00)color(red)X`

and so the other side of the line gets shaded as the solution, like this:

graph{y<2/5x-6/5 [-2.956, 8.145, -2.393, 3.154]}