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

Feb 13, 2017

Treat the inequality sign as an equal sign.

#### Explanation:

$5 x + y = 10$

$y = 10 - 5 x$

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

Feb 14, 2017

#### Explanation:

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

or $y = 10 - 5 x$

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

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

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

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

Observe that this line divides Cartesian plane in three parts.

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

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

Part 3 is the right hand side of the line. One point to the right is $\left(5 , 0\right)$ 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 $5 x + y > 10$ 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.