Question

How do you write the equation in point slope form given (1,3) and (3,-5)?

Answer 1

`y-3=-4(x-1)`

Explanation:

The equation of a line in `color(blue)"point-slope form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1)" a point on the line"`

To find m use the `color(blue)"gradient formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`
where `(x_1,y_1),(x_2,y_2)" are 2 coordinate points"`

The 2 points here are (1 ,3) and (3 ,-5)

let `(x_1,y_1)=(1,3)" and " (x_2,y_2)=(3,-5)`

`rArrm=(-5-3)/(3-1)=(-8)/2=-4`

Use either of the 2 points for `(x_1,y_1)`

`"Using " (x_1,y_1)=(1,3)" and " m=-4`

`rArry-3=-4(x-1)larrcolor(red)" in point-slope form"`