# Linear functions

• Aug 14th 2009, 03:39 PM
epetrik
Linear 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, 03:55 PM
red_dog
$g(x)=ax+b$

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

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

Now find b.
• Aug 14th 2009, 04:38 PM
epetrik
I'm still a little confused on how to solve for b.
• Aug 14th 2009, 05:14 PM
QM 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:

$y-y_1 = m(x - x_1)$
• Aug 14th 2009, 10:23 PM
HallsofIvy
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?