Find a linear function g(x) where g(4)= -1. g(x) is parallel to the line f(x) = 3x+7

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- Aug 14th 2009, 02:39 PMepetrikLinear functions
Find a linear function g(x) where g(4)= -1. g(x) is parallel to the line f(x) = 3x+7

- Aug 14th 2009, 02:55 PMred_dog
$\displaystyle g(x)=ax+b$

$\displaystyle g(4)=-1\Rightarrow 4a+b=-1$

The graph of g is parallel to the graph of f, then $\displaystyle a=3$.

Now find b. - Aug 14th 2009, 03:38 PMepetrik
I'm still a little confused on how to solve for b.

- Aug 14th 2009, 04:14 PMQM deFuturo
You can use the point-slope formula to solve this one too. You must be covering point-slope formula in your book at the moment, eh?(Nod)

You have been given a point and the slope of the line. They're not given explicitly, but you do have all the information you need. If you have a given line, and you know a second line is parallel to this line, then you know the slope of the second line. (Why?)

Using the point you are given, and the slope, use the (what I am sure must be familiar to you by now) point-slope formula:

$\displaystyle y-y_1 = m(x - x_1) $ - Aug 14th 2009, 09:23 PMHallsofIvy
red dog told you: "g(x)= ax+ b" (the general form of any linear equation) , "g(4)= 4a+ b= 1 (you were given that), and "a= 3" (because wo parallel lines have the same slope).

Replace the a in the 4a+ b= 1 by 2: 4(3)+ b= 12+ b= 1. Can you solve 12+ b= 1 for b?