Question

How do you find the slope and intercept of `x-y=1`?

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)`

The `y`-intercept of an equation in standard form is: `color(green)(C)/color(blue)(B)`

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

Therefore:

• The slope is: `m = (-color(red)(1))/color(blue)(-1) = 1`

• The `y`-intercept is: `color(green)(1)/color(blue)(-1) = -1` or `(0, -1)`

Answer 2

`1,` & x-intercept is `1` & y-intercept is `-1`

Explanation:

Given equation of straight line is

`x-y=1`

`x/1+y/-1=1`

The above equation is in standard intercept form of line: `x/a+y/b=1` which has

x-intercept: `a=1`

y-intercept: `b=-1`

The given equation of line:

`x-y=1`

`y=x-1`

The above equation is in standard slope-intercept form: `y=mx+c` with slope

`m=1`

Slope: `m=1`

Answer 3

Slope: `1`, `y`-intercept `-1`

Explanation:

Recall slope-intercept form

`y=mx+b`, with slope `m` and a `y`-intercept of `b`.

We essentially just want a `y` on the left side. Let's subtract `x` from both sides to get

`-y=-x+1`

Next, divide both sides by `-1` to get

`y=x-1`

Now, our equation is in slope-intercept form, with a slope of `1`, and a `y`-intercept of `-1`.

Hope this helps!