Question

What is the slope and intercept of `x-y=6`?

Answer 1

See a solution process below:

Explanation:

This equation is in Standard Linear form. The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

Where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

The slope of an equation in standard form is: `m = -color(red)(A)/color(blue)(B)`

`x - y = 6` is:

`color(red)(1)x + color(blue)(-1)y = color(green)(6)`

Therefore the slope is: `m = color(red)(-1)/color(blue)(-1) = 1`

To find the `y` intercept, set `x` to `0` and solve for `y`:

`x - y = 6` becomes:

`0 - y = 6`

`-y = 6`

`color(red)(-1) * -y = color(red)(-1) * 6`

`y = -6`

Therefore, the `y`-intercept is: `-6` or `(0, -6)`

If you also need the `x` intercept, do the opposite. Set `y` to `0` and solve the `x`:

`x - y = 6` becomes:

`x - 0 = 6`

`x = 6`

Therefore, the `x`-intercept is: `6` or `(6, 0)`