Question

How do you find slope, point slope, slope intercept, standard form, domain and range of a line for Line G (6,0) (9,6)?

Answer 1

slope `=2`

point-slope equation: `y-0=2(x-6)`

slope-intercept equation: `y=2x-12`

standard form equation: `y-2x=-12`

domain: `(-oo, oo)`

range: `(-oo, oo)`

Explanation:

The slope, `m`, is:

`m= (y_2 - y_1)/(x_2 - x_1) = (6-0)/(9-6)`

This is the change in `y` between the two points over the change in `x` between the two points.

Once you have found the slope, pick one of the points and plug it into the point-slope formula:

`y-y_1=m(x-x_1)`

where `y_1` is the `y`-coordinate of one of the points and `x_1` is the `x`-coordinate of the same point and `m` is the slope. In this case, it is:

`y-0=2(x-6)`

To find the slope intercept form, just solve for `y`, but in this case, since I picked the point with a `y` of `0` and `y-0=y`, that is already done so the slope-intercept form is:

`y=2x-12`

The standard form formula is

`ax+by=c`

This can be found by just subtracting `2x` from both sides of the slope-intercept equation to get:

`y-2x=-12`

Lastly, the domain and range of any straight line are negative infinity to positive infinity.

Hope I helped out!