# How do you graph 4x-5y-10<=0?

Jun 3, 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: $x = 0$

$\left(4 \cdot 0\right) - 5 y - 10 = 0$

$0 - 5 y - 10 + \textcolor{red}{10} = 0 + \textcolor{red}{10}$

$- 5 y - 0 = 10$

$- 5 y = 10$

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

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

For: $x = 5$

$\left(4 \cdot 5\right) - 5 y - 10 = 0$

$20 - 5 y - 10 + \textcolor{red}{10} = 0 + \textcolor{red}{10}$

$20 - 5 y - 0 = 10$

$20 - 5 y = 10$

$20 - \textcolor{red}{20} - 5 y = 10 - \textcolor{red}{20}$

$0 - 5 y = - 10$

$- 5 y = - 10$

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

$y = 2$ or $\left(5 , 2\right)$

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.

The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y+2)^2-0.035)((x-5)^2+(y-2)^2-0.035)(4x-5y-10)=0 [-10, 10, -5, 5]}

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

graph{(4x-5y-10) <= 0 [-10, 10, -5, 5]}