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

1 Answer
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Nov 3, 2017

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)#.

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