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

Oct 4, 2017

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: $x = 0$

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

$0 - 2 y = 10$

$- 2 y = 10$

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

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

For: $x = 2$

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

$10 - 2 y = 10$

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

$0 - 2 y = 0$

$- 2 y = 0$

$\frac{- 2 y}{\textcolor{red}{- 2}} = \frac{0}{\textcolor{red}{- 2}}$

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

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

We can now graph the inequality. Because there is no "or equal to" clause in the inequality operator we will make the line a dashes line. And, we can shade the left side of the line for the "less than" inequality operator.

graph{5x-2y-10 < 0 [-20, 20, -10, 10]}