Question

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

Answer 1

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`

`(5 * 0) - 2y = 10`

`0 - 2y = 10`

`-2y = 10`

`(-2y)/color(red)(-2) = 10/color(red)(-2)`

`y = -5` or `(0, -5)`

For: `x = 2`

`(5 * 2) - 2y = 10`

`10 - 2y = 10`

`-color(red)(10) + 10 + 2y = -color(red)(10) + 10`

`0 - 2y = 0`

`-2y = 0`

`(-2y)/color(red)(-2) = 0/color(red)(-2)`

`y = 0` or `(2, 0)`

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]}