Question

What is the equation of a line, in point-slope form, that passes through (−2, −6) (−2, −6) and has a slope of  1/3?

Answer 1

point-slope form is y - y1 = m(x - x1)

plug in the given slope and the given point

y - (-6) = (1/3)(x - (-2))

then simplify

y + 6 = (1/3)(x + 2)

Answer 2

`y+6=(1)/(3)(x+2)`

Explanation:

General equation of point slope form :
`y-y_1=m(x-x_1)`

where m is the slope

Point =
`(x_1,y_1)=(-2,-6)`

Slope =
`m = (1)/(3)`

Substitute the values in general form of point slope form .

`y-y_1=m(x-x_1)`

`y-(-6)=(1)/(3)(x-(-2))`

`y+6=(1)/(3)(x+2)`

This can be simplified further

`y+6=(1)/(3)x+(2)/(3)`

`y=(1)/(3)x+(2)/(3)-6`

`y=(1)/(3)x-(16)/(3)`

Hence the equation of a line, in point-slope form, that passes through (−2, −6) and has a slope of 1/3 is
`y+6=(1)/(3)(x+2)`