Question

How do you write the point slope form of the equation given (1,12) and (-3,5)?

Answer 1

`y-12=7/4(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 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 are "(x_1,y_1)=(1,12),(x_2,y_2)=(-3,5)`

`rArrm=(5-12)/(-3-1)=(-7)/(-4)=7/4`

`"use either of the 2 given points as point on line"`

`"using "m=7/4" and "(x_1,y_1)=(1,12)" then"`

`y-12=7/4(x-1)larrcolor(red)" in point-slope form"`