Question

How do you graph `x-6y+3>0`?

Answer 1

Everything below the line `y=\frac{x}{6}+\frac{1}{2}`, excluding the line.

Explanation:

To make this easier, make the inequality a function of y. First, add `6y` to both sides and simplify.
`6y< x+3`
`y<\frac{x+3}{6}`

Plotting the function gives you the following graph
graph{(x+3)/6 [-10, 10, -5, 5]}
Since the inequality states that y is less than the value of the functions, we shade in everything below the line and make it a dashed line.