# How do you graph the linear inequality -2x - 5y<10?

Mar 13, 2018

See a solution process below:

#### Explanation:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For: $x = 0$

$\left(- 2 \cdot 0\right) - 5 y = 10$

$0 - 5 y = 10$

$- 5 y = 10$

$\frac{- 5 y}{\textcolor{red}{- 5}} = \frac{10}{\textcolor{red}{- 5}}$

$y = - 2$ or $\left(0 , - 2\right)$

For: $y = 0$

$- 2 x - \left(5 \cdot 0\right) = 10$

$- 2 x - 0 = 10$

$- 2 x = 10$

$\frac{- 2 x}{\textcolor{red}{- 2}} = \frac{10}{\textcolor{red}{- 2}}$

$x = - 5$ or $\left(- 5 , 0\right)$

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{(x^2+(y+2)^2-0.05)((x+5)^2+y^2-0.05)(-2x-5y-10)=0 [-10, 10, -5, 5]}

Now, we can shade the rightside of the line.

The boundary line will need to be changed to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(-2x-5y-10) < 0 [-10, 10, -5, 5]}