Question

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

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`

`(4 * 0) - 5y - 10 = 0`

`0 - 5y - 10 + color(red)(10) = 0 + color(red)(10)`

`-5y - 0 = 10`

`-5y = 10`

`(-5y)/color(red)(-5) = 10/color(red)(-5)`

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

For: `x = 5`

`(4 * 5) - 5y - 10 = 0`

`20 - 5y - 10 + color(red)(10) = 0 + color(red)(10)`

`20 - 5y - 0 = 10`

`20 - 5y = 10`

`20 - color(red)(20) - 5y = 10 - color(red)(20)`

`0 - 5y = -10`

`-5y = -10`

`(-5y)/color(red)(-5) = -10/color(red)(-5)`

`y = 2` or `(5, 2)`

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]}