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

See below

#### Explanation:

Let's solve this inequality for $y$:

$2 x > 5 y + 6$

$5 y < 2 x - 6$

$y < \frac{2 x - 6}{5} = \frac{2}{5} x - \frac{6}{5}$

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 $\left(0 , - \frac{6}{5}\right)$ which is the $y$-intercept and also point $\left(0 + 5 , - \frac{6}{5} + 2\right) \implies \left(5 , \frac{4}{5}\right)$ 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 $\left(0 , 0\right)$ to see if the inequality works with this value:

$0 < \frac{2 \left(0\right) - 6}{5}$

$0 < - \frac{6}{5} \textcolor{w h i t e}{00} \textcolor{red}{X}$

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]}