Question

How do you write an equation in point slope form given slope 2/3, (5,6)?

Answer 1

The linear equation in point slope form is `y-6=2/3(x-5)`.

Explanation:

The general equation for a line in point slope form is `y-y_1=m(x-x_1)`, where `m="slope"=2/3"`, `x_1=5`, and `y_1=6`.

To get the point slope form for the variables given, plug the known values into the equation.

`y-6=2/3(x-5)`

________

Now, if you wish, you can determine the slope intercept form for easier graphing, by solving the point slope form for `y`. This will give the x and y interceptss, where the x-intercept is the value of `x` when `y=0`, and the y-intercept is the value of `y` when `x=0`. Once you have the x and y intercepts, you only need to plot two points to graph the line.

The general equation for the slope intercept form is `y=mx+b`, where `m` is the slope, `(2/3)`, and `b` is the y-intercept.

Start with the point slope form and solve for `y`.

`y-6=2/3(x-5)`

Add `6` to both sides.

`y=2/3(x-5)+6`

Simplify.

`y=2/3x-10/3+6`

Multiply `6` by `3/3` to get `18/3`.

Simplify.

`y=2/3x-10/3+18/3`

Simplify.
The slope intercept form is `y=2/3x+8/3`, where the slope, `m`, is `2/3`, and the y-intercept is `8/3` and the point is `(0,8/3)`.

To find the x-intercept , make `y=0` and solve for `x`.

`0=2/3x+8/3`

`-2/3x=8/3`

`-6x=24`

`x=24/(-6)`

`x=-4`

The x-intercept is `-4` and the point is `(-4,0)`.

graph{y=2/3x+8/3 [-10, 10, -5, 5]}