Getting a line in slope-intercept form means solving for y and getting everything else to the other side.
With the equation in the form `x=3y-5` , we need to have anything that doesn't look like y to go to the other side. And, although it doesn't matter which order you do the operations in, it is usually a little easier if you move stuff furthest from y first.
`x=3y-5` we usually have the y by itself on the left
`3y-5=x` add 5 to both sides
`3y=x+5` now divide both sides by 3
`y=1/3 x + 5/3` we are done!
This means the slope is `m=1/3` and the y-intercept is `b=5/3` .
The slope-intercept form of the line is `y=1/3x+5/3` .
You should remember that slope intercept form of equation of a line is `y = -(B/A)x - (C/A) => y = mx + n` .
`m = -B/A` (slope of line)
`n = -C/A` (y intercept)
Comparing the given form to the slope intercept form yields that you need to isolate the term that contains y to the left side such that:
`3y = x + 5`
You need to divide by 3 both sides such that:
`y = (1/3)x + 5/3`
Hence, putting the given equation in the slope intercept form yields `y = (1/3)x + 5/3` .