# How do you graph x+5y<=10 on the coordinate plane?

Aug 19, 2017

See a solution process below:

#### Explanation:

First, change the inequality to a quality and find two points that are solutions to the equality:

For $x = 0$:

$0 + 5 y = 10$

$5 y = 10$

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

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} y}{\cancel{\textcolor{red}{5}}} = 2$

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

For $y = 0$

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

$x + 0 = 10$

$x = 10$ or $\left(10 , 0\right)$

We can now plot the two points on the grid and draw a line through the points to draw the boundary of the inequality:

graph{(x^2+(y-2)^2-0.025)((x-10)^2+y^2-0.025)(x+5y-10)=0 [-12, 12, -6, 6]}

Because it is an inequality and the operator is "less than or equal to" the line will remain solid for graphing the inequality.

And, because it is a "less than" inequality we will shade to the left of the line.

graph{(x+5y-10)<=0 [-12, 12, -6, 6]}