Question

How do you write the equation in point slope form given (-3,-5) and (3,-15)?

Answer 1

`y+5=-5/3(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)=(-3,-5)" and "(x_2,y_2)=(3,-15)`

`rArrm=(-15-(-5))/(3-(-3))=(-10)/6=-5/3`

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

`"using "m=-5/3" and "(x_1,y_1)=(-3,-5)`

`y-(-5)=-5/3(x-(-3))`

`rArry+5=-5/3(x+3)larrcolor(red)"in point-slope form"`

Answer 2

`(y+5)=-5/3(x+3)`

Explanation:

Point slope form is `(y-y_1)=m(x-x_1)`
First, find the slope by using `m=(y_1-y_2)/(x_1-x_2)`
`(-15+5)/(3+3)=-10/6=-5/3=m`
Then, choose one of the coordinate pairs (let's use `-3,-5`) and plug those in for `y_1` and `x_1` and also plug in the slope for `m`.
We get: `(y+5)=-5/3(x+3)`