Question

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

Answer 1

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`

`(10 * 0) + 2y = 14`

`0 + 2y = 14`

`2y = 14`

`(2y)/color(red)(2) = 14/color(red)(2)`

`y = 7` or `(0, 7)`

For `x = 2`

`(10 * 2) + 2y = 14`

`20 + 2y = 14`

`-color(red)(20) + 20 + 2y = -color(red)(20) + 14`

`0 + 2y = -6`

`2y = -6`

`(2y)/color(red)(2) = -6/color(red)(2)`

`y = -3` or `(2, -3)`

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]}