# How do you graph the inequality -5x+2y<-6?

##### 1 Answer
May 28, 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: $x = 0$

$\left(- 5 \cdot 0\right) + 2 y = - 6$

$0 + 2 y = - 6$

$2 y = - 6$

$\frac{2 y}{\textcolor{red}{2}} = - \frac{6}{\textcolor{red}{2}}$

$y = - 3$ or $\left(0 , - 3\right)$

For: $x = 2$

$\left(- 5 \cdot 2\right) + 2 y = - 6$

$- 10 + 2 y = - 6$

$\textcolor{red}{10} + 10 + 2 y = \textcolor{red}{10} + - 6$

$0 + 2 y = 4$

#2y = 4

$\frac{2 y}{\textcolor{red}{2}} = \frac{4}{\textcolor{red}{2}}$

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

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+3)^2-0.125)((x-2)^2+(y-2)^2-0.125)(-5x+2y+6)=0 [-20, 20, -10, 10]}

Now, we can shade the left side of the line.

We need to change the boundary to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(-5x+2y+6) > 0 [-20, 20, -10, 10]}