Question

How do you write the point slope form of the equation given (4,2) and (1,-1)?

Answer 1

`y-2=(x-4)`

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 calculate 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 (4 ,2) and (1 ,-1)

let `(x_1,y_1)=(4,2)" and " (x_,y_2)=(1,-1)`

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

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

`"Using " (4,2)=(x_1,y_1)" and " m=1`

`y-2=1(x-4)larrcolor(red)" in point slope form"`