Question

What is the equation of a line with a slope of 1/3 that passes through the point (-1, 6)?

Answer 1

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

Explanation:

The point-slope formula is
`y -y_(1) =m(x -x_(1))` where we substitute a point (x,y) for
`(x_(1),y_(1))`.

We have m=
`(1)/(3)` and (-1, 6). We input m and
`x_(1) =-1\\y_(1)=6`.

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

We can convert into the slop-intercept from by simplifying the parenthesis and solving for y.

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