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

Nov 3, 2017

Possible Answer: $g \left(x\right) = 2 x + 4$

#### Explanation:

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

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 $g \left(x\right) = 2 x + b$ (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 $g \left(x\right) = 2 x + 4$, which is both steeper than the parent function and is shifted 4 units up (from a y-intercept of $\left(0 , 0\right)$ to $\left(0 , 4\right)$.