Question

How do you write the equation in point slope form given (3, 4) and (–3, –8)?

Answer 1

`y-4=2(x-3)`

Explanation:

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

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

We require to find m. To do this we can use the `color(blue)"gradient formula"`

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

The 2 points here are (3 ,4) and (-3 ,-8)

let `(x_1,y_1)=(3,4)" and " (x_2,y_2)=(-3,-8)`

`rArrm=(-8-4)/(-3-3)=(-12)/(-6)=2`

We now have m = 2 and using either of the 2 given points, we can obtain the equation.

substitute m = 2 and `(x_1,y_1)=(3,4)" into (A)"`

`y-4=2(x-3)" equation in point-slope form"`