Question

What is the point slope form of the equation (-6,6), (3,3)?

Answer 1

see below.

Explanation:

First, we need to find gradient of slope that cross between `(-6,6)` and `(3,3)` and denotes as `m`. Before this let `(x_1,y_1)=(-6,6)` and `(x_2,y_2)=(3,3)`

`m=(y_2-y_1)/(x_2-x1)`
`m=(3-6)/(3-(-6))`
`m=-1/3`

According to "http://www.purplemath.com/modules/strtlneq2.htm", the point slope form is `y-y_1=m(x-x_1)`

From above, using `(-6,6)` the point slope form is `y-6=-1/3(x-(-6))` and simplied it becomes `y=-1/3x+4`

How about second point? It produce same answer as equation that using the first points.

`y-3=-1/3(x-3)`
`y-3=-1/3x+1`
`y=-1/3x+4` (prove)

Answer 2

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

Explanation:

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

`•color(white)(x)y-y_1=m(x-x_1)`

`"where m is the slope and "(x_1,y_1)" a point on the line"`

`"to calculate m use the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(-6,6)" and "(x_2,y_2)=(3,3)`

`rArrm=(3-6)/(3-(-6))=(-3)/9=-1/3`

`"using "m=-1/3" and "(x_1,y_1)=(3,3)" then"`

`y-3=-1/3(x-3)larrcolor(red)"in point-slope form"`