Question

Graph x-y=2. I understand why it is -2 on y-axis, but why is it "2" on the x-axis?

Answer 1

`"see explanation"`

Explanation:

`"How to find where "x-y=2" crosses the x and y axes"`

`•  "For the y-intercept, let x = 0 in the equation "`

`• "For the x-intercept, let y = 0 in the equation "`

Let `x=0`
`x-y=2`
`0-y=2`
`y=-2larrcolor(red)"y-intercept"`

Let `y=0`
`x-y=2`
`x - 0=2`
`x = 2larrcolor(red)"x-intercept"`

`"Plot the points" (0,`-`2)" and (2,0)`
`"and draw a straight line through them to graph"`
graph{(y-x+2)((x-0)^2+(y+2)^2-0.04)((x-2)^2+(y-0)^2-0.04)=0 [-10, 10, -5, 5]}

Answer 2

The `x` intercept is the place on the `x` axis where `y` is `0`.
`x - y   = 2`

`x - 0   = 2`

`x`  ░░  `= 2`

`(2,0) larr` coordinates for the `x` intercept

Explanation:

You can graph this line in a couple of ways.

One way is to turn the equation into the slope-intercept form of the equation, which is `y = mx + b`

Another way is to plot both intercepts and draw the line through these points.

Finding the y intercept
`x - y = 2`

The `y` intercept is the place where the line crosses the `y` axis.
This is automatically the place where `x=0`

One trick to finding the `y` intercept is to make `x` go to zero just by covering up the entire `x` term with your fingertip.
Then solve for `y`.

`x - y = 2`

Cover up `x` with your fingertip

░░ `- y = 2`

Now it's pretty easy to see that `y =-2`
That gives you the coordinates of the `y` intercept, the place where `x` is `0`
`(0,`-`2)` `larr` the `y` intercept

`color(white)(mmmmmmm)` ―――――――――――

And here is the good part.
You can use the exact same trick to find the `x` intercept.

Finding the `x` intercept

The `x` intercept is the place where `y = 0`

You can solve the equation for `x` by subbing in `0` in the place of `y`
`x - y = 2`
`x - 0 = 2`
`x = 2`

Or you can just solve it visually by covering the entire `-y` term with your fingertip and seeing the answer.
`x - y  = 2`
`x     ░░ = 2`

So the coordinates for the `x` intercept are `(2,0)`

`color(white)(mmmmmmm)` ―――――――――――

This "fingertip" trick is especially useful where there are coefficients for `x` and `y`.

Example:
`2x - 3y = 12`

When you let `x` equal `0`, the entire `x` term drops out
░░ `-3y = 12`

And when you let `y` equal `0`, the entire `y` term drops out
`2x` ░░ `= 12`

This trick lets you rapidly solve for `x` and `y`.
Often you can solve it instantly just in your head.