Question

How do you write the point slope form of the equation given (-3,4) and (0,3)?

Answer 1

`y-3=-1/3(x-0)`

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)|)))`
where m represents the slope and `(x_1,y_1)` a point on the line.

To calculate the slope 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 `(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points".`

here the 2 points are (-3 ,4) and (0 ,3)

let `(x_1,y_1)=(-3,4)" and " (x_2,y_2)=(0,3)`

`rArrm=(3-4)/(0+3)=-1/3`

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

Using (0 ,3) and m`=-1/3` substitute these values into the point-slope equation.

`y-3=-1/3(x-0)larr" point-slope form"`

If we distribute the brackets and rearrange .

or `y=-1/3x+3larr" slope-intercept form"`