Question

How do you write the equation of a line in point slope form that is parallel to `y=2/3x+9` and goes through (4,8)?

Answer 1

The answer is `y=2/3x+16/3`

The function we are looking form is a linear function, so it can be written as `y=ax+b`.
The line is parallel to `y=2/3x+9` so `a=2/3` (If 2 lines are parallel their `a` coefficients are equal).
Now we have to calculate `b` knowing that the line goes through `(4,8)` so you can substitute 4 for `x` and 8 for `y` and solve the equation for `b`.

The equation is `8=2/3*4+b`, so `b=8-2/3*4`
`b=24/3-8/3`
`b=16/3`

So the final answer is `y=2/3x+16/3`