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

Question

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

1. y+2=1/3(x+6)
2. y−2=1/3(x−6)
3. y+6=1/3(x+2)
4. y−6=1/3(x−2)

Answer 1

Hello!

You need to use the Point slope formula

y-y1=m(x-x1)

Plug your point into the equation with the slope (m)

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

Then simplify

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

Answer 2

from the choices - it is y + 6 = 1/3(x+2)

why ?

the point / slope format of an equation is y = mx + b

in this case, the slope which is m in the equation is given as 1/3; x is given as -2 and y is given as -6

let's plug all this in and solve for the missing piece b

-6 = 1/3(-2) + b

When you multiply 1/3 by -2 you get

-6=-2/3+b

when you shift the -2/3 from the right side of the equation by adding it to the left hand side, the result is b = -16/3

like this

-6 + 2/3 = b

get the lcd (3)

and you have

-18/3 + 2/3 = b

-16/3 = b

when you work out the equation in the first line I wrote above you get

y = 1/3x - 16/3 for the general equation of the line.

Answer 3

the 3rd choice is probably correct.

although as written they are a little ambiguous.

if they are meant to mean that the right side is 1/3 times the expression in parentheses then 3rd