Question

How do you write the equation in point slope form given (2, 5) (3,10)?

Answer 1

`y-5=5(x-2)`

Explanation:

In general, given two points `(x_1,y_1)` and `(x_2,y_2)`
the slope can be calculated as
`color(white)("XXX")m=(y_2-y_1)/(x_2-x_1)`

and the equation of the line through these points using the point slope form is
`color(white)("XXX")(y-y_1)=m(x-x_1)color(white)("XXXXX")`see below for other forms

Given
`color(white)("XXX")(x_1,y_1)=(2,5)` and
`color(white)("XXX")(x_2,y_2)=(3,10)`

`m=(10-5)/(3-2)=5`

and the slope point form of the equation is
`color(white)("XXX")y-5=5(x-2)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The "slope-point form" may also appear in the form:
`color(white)("XXX")y-y_2=m(x-x_2)`
or
`color(white)("XXX")(y-y_1)/(x-x_1)=m`
or
`color(white)("XXX")(y-y_2)/(x-x_2)=m`
All these forms are equivalent.

Answer 2

`y-5=5(x-2)`

graph{y=5x-5 [-10, 10, -5, 5]}

Explanation:

The point gradient/slope form is

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

Were `y_1 and x_1` are points in which the line goes through, with `x_1` being the x position and `y_1` the y position which the points go through . Obviously the line goes through two of these points but lets just use `(2,5)` as the point.

Next, we need the gradient which is `(rise)/(run)`. The rise between the two points are 5, with the run being 1. therefore, the gradient is `5`

Now with these values, we substitute it into the equation to get an answer in point gradient/slope from.