How do you graph the inequality 10x+2y<=14?

Aug 23, 2017

See a solution process below:

Explanation:

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

For $x = 0$

$\left(10 \cdot 0\right) + 2 y = 14$

$0 + 2 y = 14$

$2 y = 14$

$\frac{2 y}{\textcolor{red}{2}} = \frac{14}{\textcolor{red}{2}}$

$y = 7$ or $\left(0 , 7\right)$

For $x = 2$

$\left(10 \cdot 2\right) + 2 y = 14$

$20 + 2 y = 14$

$- \textcolor{red}{20} + 20 + 2 y = - \textcolor{red}{20} + 14$

$0 + 2 y = - 6$

$2 y = - 6$

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

$y = - 3$ or $\left(2 , - 3\right)$

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 a "or equal to" clause.

graph{(x^2+(y-7)^2-0.125)((x-2)^2+(y+3)^2-0.125)(10x+2y-14)=0 [-20, 20, -10, 10]}

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

graph{(10x+2y-14)<=0 [-20, 20, -10, 10]}