Question

What is the equation for a line that is steeper than the parent function `f(x) =x` and shifted up four?

Answer 1

Possible Answer: `g(x)=2x+4`

Explanation:

Note that the given equation, `f(x)=x` has slope of `m=1` and y-intercept at `(0,0)`.

Since the greater the slope `m`, the steeper the line, we can let `m` be any value greater than `1`, say `2`, so we now have that `g(x)=2x+b` (continue reading for further information on `b`, the y-intercept)

To move the line up `4` units, we can add `4` to our function to get `g(x)=2x+4`, which is both steeper than the parent function and is shifted 4 units up (from a y-intercept of `(0,0)` to `(0,4)`.