Question

How do I find an equation of the line using function notation that goes through (5,8) parallel to `f(x)= 3x- 8`?

Answer 1

`y-8 = 3(x-5)` or, in standard form, `3x-y= 7`
or in functional notation `f(x) = 3x-7`

Explanation:

`f(x)=3x-8` is the equation of a line in slope-intercept form with a slope of `3`.

All lines parallel to `f(x)=3x-8` have the same slope.

Temporarily, writing `y` in place of `f(x)` :
the equation of a line through `(hatx,haty)=(5,8)` with a slope of `m=3` can be written in point slope form as:
`color(white)("XXXX")` `(y-haty)= m(x-hatx)`
or
`color(white)("XXXX")` `(y-8) = 3(x-5)`

We can simplify this:
multiplying through the right side:
`color(white)("XXXX")` `y-8 = 3x-15`
subtracting `y` from both sides:
`color(white)("X8XXX")` `-8 = 3x -15 -y`
adding `15` to both sides
`color(white)("XXXX")` `7 = 3x-y`

Or, going back to `y-8=3x-15` and restoring `f(x)` for `y`:
`color(white)("XXXX")` `f(x)-8 = 3x-15`
`color(white)("XXXX")` `f(x)= 3x-7`