Question

How do you graph `y = -x-2` by plotting points?

Answer 1

You find ordered pairs by assigning various values to `x` and then calculating `y.` You plot those ordered pairs and draw the resulting line.

Explanation:

You can create an endless set of ordered pairs from the equation.
You just pick values for `x`, then solve for `y`.

In theory, you need only two points to define a line, but it's better to have three points. New students should solve for five points until they are used to this work.

1) For the values of `x`,
- Choose a couple of values higher than zero
- Choose `x = 0`
- Choose a couple of values lower than zero

2) For example, you could choose these values for `x`:
6, 2, 0 , ⎯ 2, ⎯ 6

3) To turn them into ordered pairs that you can plot, sub each value into the given equation
`y=−x−2`

When `x = 6`
`y = - 6 - 2`
`y = -8`
(6,⎯ 8) <-- an ordered pair

When `x = 2`
`y = - 2 - 2`
`y = -4`
(2,⎯ 4) <-- another ordered pair

When `x = 0` <-- this is the y intercept
`y = - 0 - 2`
`y = -2`
(0,⎯ 2) <-- a third ordered pair, the y intercept

When `x = ⎯ 2`
`y = - (⎯ 2) - 2`
`y = 0`
(⎯ 2,0) <-- This turned out to be the x intercept

When `x = -6`
`y = - (-6) - 2`
`y = 4`
(⎯ 6,4) <-- the fifth ordered pair

Plot these points by marking delicate dots or crosses on a graph.
Connect the dots with a thin delicate line.
Don't make big dark dots or thick dark lines.

If one of the dots does not lie on the line, that means that there was a mistake, so go back and figure out the ordered pair over again.

You can predict what the resulting line will look like by looking at the original equation. In this case, you can see three facts:
- The y intercept will be at (0,-2) because that is the value of b in the equation
- The line is going downhill because the slope m is negative (`-x`)
- The downhill slope is not steep because the value of m is only `-1`

You can Google the original equation and get an image of the line.
https://www.google.com/search?source=hp&ei=6tMKWrzUNYnxmAHEt5CQCg&q=y+%3D+-x+-2&oq=y
The blue dot is interactive, so you can slide it up and down until you get the values of `x` that you chose. Then you can read the values of `y` at that point.