Question

How do you graph the inequality `5x+y>10`?

Answer 1

Treat the inequality sign as an equal sign.

Explanation:

`5x+y=10`

`y=10-5x`

Now, just pick your values for x and solve for y!

Answer 2

Please see below.

Explanation:

Let us first consider the equality i.e. `5x+y=10`

or `y=10-5x`

Now, just pick values for `x` and solve for `y`

Let us pick `x=0,2` and `4`

As `y=10-5x`, `y=10,0` and `-10`

and joining points `(0,10)`, `(2,0)` and `(4,-10)` we get following graph.
graph{10-5x [-20, 20, -10, 10]}
But this is still not the graph for `5x+y>10`

Observe that this line divides Cartesian plane in three parts.

Part 1 is the line itself and we know on the line `5x+y=10` and hence line is not the solution.

Part 2 is the left hand side of the line. One point on the left is `(0,0)` and if we put these values of `x` and `y` we get `0`, which is less than `10`. Hence in Part 2, we have `5x+y<10`. This too is not a solution as what we need is `5x+y>10`.

Part 3 is the right hand side of the line. One point to the right is `(5,0)` and if we put these values of `x` and `y` we get `25`, which is greater than than `10`. Hence in Part 2, we have `5x+y>10` and this is the solution and it looks like
graph{5x+y>10 [-20, 20, -10, 10]}
Observe that line is dashed , which shows that points on the line do not form the solution.